Heat-pulse (HP) methods based on Marshall’s theory have been widely used in sapflow meters to measure plant water uptake since the 1950s. Some of the popular HP methods include (i) the compensation heat pulse (CHP) method, (ii) the T-max method, and (iii) the heat ratio (HR) method. Most other sap flow methods use some variations of these basic methods. Although all these methods are based on the same theory, in practice, their accuracy varies depending on the estimated HP velocity. Some of the often cited reasons for the differences in the performance of these methods are (i) wound effect, (ii) asymmetrical spacing of temperature probes, (iii) low logging frequency, (iv) sensor resolution, (v) electronic noise, (vi) drift in temperature measurements, etc. However, it is unclear why these error artifacts affect the performance of different methods at different HP velocity ranges. Here, we use mathematical model simulations to show that the presence of noise in temperature measurements constrains the measurable range of HP velocities of these different methods depending on the noise intensity. Using Monte Carlo simulations we quantitatively assess the accuracy of these methods. While typical HP measurements log temperature data every second for about 3 min, most HP methods only use a few data points. We show that when the signal-to-noise ratio (SNR) of these chosen data points is small, the accuracy suffers. By employing a sum of squares error minimization (SSEM) approach that minimizes the errors between observed and model-predicted temperatures using all the observed data points, we show that noise induced errors in sap flow measurement can be virtually eliminated over a range of conditions. Our findings provide a mechanistic understanding of the origins and impacts of the noise-induced errors in sap flow measurements and the mathematical framework to overcome the same.

中文翻译：

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基于热脉冲的液流测量方法中的噪声引起的误差

自 20 世纪 50 年代以来，基于马歇尔理论的热脉冲 (HP) 方法已广泛应用于液流计来测量植物吸水量。一些流行的 HP 方法包括 (i) 补偿热脉冲 (CHP) 方法、(ii) T-max 方法和 (iii) 热比 (HR) 方法。大多数其他液流方法使用这些基本方法的一些变体。尽管所有这些方法都基于相同的理论，但在实践中，它们的精度根据估计的 HP 速度而变化。这些方法性能差异的一些经常被引用的原因是（i）伤口效应，（ii）温度探头的不对称间距，（iii）记录频率低，（iv）传感器分辨率，（v）电子噪声， (vi) 温度测量的漂移等。然而，尚不清楚为什么这些误差伪影会影响不同方法在不同 HP 速度范围下的性能。在这里，我们使用数学模型模拟来表明，温度测量中噪声的存在限制了这些不同方法的 HP 速度的可测量范围，具体取决于噪声强度。使用蒙特卡罗模拟，我们定量评估这些方法的准确性。虽然典型的 HP 测量每秒记录大约 3 分钟的温度数据，但大多数 HP 方法仅使用几个数据点。我们表明，当这些所选数据点的信噪比 (SNR) 较小时，准确性会受到影响。通过采用误差平方和最小化 (SSEM) 方法，使用所有观测数据点最小化观测温度和模型预测温度之间的误差，我们表明，在一系列条件下，液流测量中的噪声引起的误差几乎可以消除。我们的研究结果提供了对液流测量中噪声引起的误差的起源和影响的机械理解，以及克服该误差的数学框架。