VFLUX: Vertical Fluid Heat Transfer Solver (VFlu[H]X Solver)

VFLUX is a program that calculates one-dimensional vertical fluid flow (seepage flux) through saturated porous media, using heat transport equations. It uses temperature time series data measured by multiple temperature sensors in a vertical profile in order to calculate flux at specific times and depths. VFLUX is written as a MATLAB toolbox, a set of functions that run in the MATLAB environment.

Please cite as: (Gordon et al., 2012; Irvine et al., 2015)
- Irvine, DJ, LK Lautz, MA Briggs, RP Gordon, JM McKenzie. 2015. Experimental evaluation of the applicability of phase, amplitude, and combined methods to determine water flux and thermal diffusivity from temperature time series using VFLUX 2. Journal of Hydrology, 531(3):728-737. doi:10.1016/j.jhydrol.2015.10.054.
- Gordon, RP, LK Lautz, MA Briggs, JM McKenzie. 2012. Automated calculation of vertical pore-water flux from field temperature time series using the VFLUX method and computer program. Journal of Hydrology, 420-421:142-158. doi: 10.1016/j.jhydrol.2011.11.053.
- (Two minor typographical errors were recently discovered in the publication Gordon et al. (2012). The definition for H in Equation 12 (p. 147) should be corrected to read “H = Cw/λo”. Also, Equation 9 (p. 147) should read “κe = (λo/C) + β|v|”, where v is the thermal front velocity. Please note that the code of the VFLUX program has always contained the correct forms of these two equations. Thanks go to Chengpeng Lu of Hohai University and Dylan Irvine of Monash University for bringing these typographical errors to our attention.)

VFLUX 1.2.5: The original VFLUX code, with amplitude- and phase-based solutions to determine flux from temperature time series data, as well as signal processing methods, data visualization, sensitivity analysis, and Monte Carlo error analysis modules.

VFLUX 2.0.0: Includes all functionality of the original VFLUX, with the addition of solutions for the “combined” amplitude ratio and phase lag methods (Luce et al., 2013; McCallum et al., 2012). More information can be found in Irvine et al. (2015).

VFLUX requires the Captain Toolbox and the ‘resample’ function from the MATLAB Signal Processing Toolbox. The Captain Toolbox is available for free at http://www.lancs.ac.uk/staff/taylorcj/tdc/download.php. The Signal Processing toolbox is available from MathWorks at http://www.mathworks.com/products/signal/. If the Signal Processing Toolbox is not available to you, then an alternate function may be substituted (for more information, contact the authors).

VFLUX Add-ons
(1) vflux_qar_opt is an add on program for VFLUX2 (v 2.0.0 and greater). vflux_qar_opt has two main applications: 1) to fine tune flux estimates using the benefits of two analytical solutions, and 2) to provide a workflow to assess potential streambed scour. vflux_qar_opt can be run after the main vflux functions, where the user can optimize flux estimates by refining the thermal diffusivity (κe) value that best reproduces the known sensor spacing (Δz). More information can be found in the vflux_qar_opt documentation, which is included with the m-file in the download, and associated manuscript (Irvine et al. 2017).
Irvine, DJ, MA Briggs, I Cartwright, CR Scruggs, LK Lautz. 2017. Improved vertical streambed flux estimation using multiple diurnal temperature methods in series. Groundwater, 55(1): 73-80. doi: 10.1111/gwat.12436

VFLUX是一款基于热输运方程（heat transport equations），计算饱和多孔介质中一维垂直流体渗流通量（seepage flux）的程序。它利用垂直剖面内多台温度传感器实测的温度时间序列数据，来计算特定时刻与深度处的渗流通量。VFLUX被编写为MATLAB工具箱，即一组可在MATLAB环境中运行的函数集。

请按以下文献引用：（Gordon等，2012；Irvine等，2015）
- Irvine, DJ, LK Lautz, MA Briggs, RP Gordon, JM McKenzie. 2015. 基于VFLUX 2的温度时间序列测定水通量与热扩散率（thermal diffusivity）的相位、振幅及联合方法适用性实验评估. 《水文学杂志》, 531(3):728-737. doi:10.1016/j.jhydrol.2015.10.054.
- Gordon, RP, LK Lautz, MA Briggs, JM McKenzie. 2012. 利用VFLUX方法与计算机程序从野外温度时间序列自动计算垂直孔隙水通量. 《水文学杂志》, 420-421:142-158. doi: 10.1016/j.jhydrol.2011.11.053.
（注：近期在Gordon等(2012)的发表文献中发现两处排版错误：第147页的公式12中H的定义应更正为“H = Cw/λo”；此外第147页的公式9应更正为“κe = (λo/C) + β|v|”，其中v为热锋面速度（thermal front velocity）。请注意VFLUX程序的代码始终包含这两个公式的正确形式。感谢河海大学陆承鹏与莫纳什大学Dylan Irvine指出这些排版错误。）

VFLUX 1.2.5：初始版本的VFLUX代码，包含基于振幅与相位的温度时间序列通量求解方案，同时集成了信号处理（signal processing）、数据可视化（data visualization）、敏感性分析（sensitivity analysis）以及蒙特卡洛误差分析（Monte Carlo error analysis）模块。
VFLUX 2.0.0：保留了初始VFLUX的全部功能，新增了“联合”振幅比与相位滞后方法的求解方案（Luce等，2013；McCallum等，2012）。更多详细信息可参考Irvine等(2015)的研究。

VFLUX需依赖Captain工具箱与MATLAB信号处理工具箱（Signal Processing Toolbox）中的‘resample’函数。Captain工具箱可通过http://www.lancs.ac.uk/staff/taylorcj/tdc/download.php 免费获取；MATLAB信号处理工具箱可从MathWorks公司获取，地址为http://www.mathworks.com/products/signal/。若无法获取MATLAB信号处理工具箱，可使用替代函数（如需更多信息，请联系作者）。

VFLUX附加组件
(1) vflux_qar_opt 是面向VFLUX2（2.0.0及更高版本）的附加程序。vflux_qar_opt主要有两大应用场景：1）结合两种解析解的优势对通量估算结果进行精细化调整；2）提供一套工作流以评估潜在的河床冲刷（streambed scour）情况。用户可在主VFLUX函数运行完成后调用vflux_qar_opt，通过优化热扩散率（κe）参数值，使其最贴合已知的传感器间距（Δz），从而优化通量估算结果。更多详细信息可参考下载包中m文件附带的vflux_qar_opt文档，以及相关研究论文（Irvine等，2017）。
Irvine, DJ, MA Briggs, I Cartwright, CR Scruggs, LK Lautz. 2017. 基于连续多日温度方法改进垂直河床通量估算. 《地下水》, 55(1): 73-80. doi: 10.1111/gwat.12436