Solar Water Disinfection: A Probabilistic Methodology for Extracting Exposure Period from Time Series of Insolation Data

The operation of solar disinfection (SODIS) systems require a variable exposure period depending upon a number of process parameters: cloud coverage, air temperature, water turbidity, and pathogen concentration. The uncertainty arising from variable exposure period can be resolved using probability methods. The study presents a probabilistic methodology for extracting exposure period from times series of insolation data. To do this, the exposure period was interpreted as the number of consecutive exposure days until the occurrence of a day whose solar irradiance is higher than the disinfection threshold. This interpretation is consistent with the underlying physical processes that govern geometric distribution. Representative values of monthly exposure periods can be selected for any locations at a given probability of exceedance, assuming geometric distribution. The 3600 data samples are contained in the folder “ The 3600 Data Samples for the 300 Locations, January to December”. The excel workbooks in the data sample folder are named by the latitude, longitude, and month for which the data represent. “Result of Anderson-Darling Goodness-of-Fit Test and Model Validation” contains a table of results obtained from the Anderson-Darling goodness-of-fit test and model validation for the 3600 data samples collected for different locations and months (300 locations multiplied by 12 months). The same results were reproduced in the form of maps in “Goodness of Fit Maps”, “Observed vs Predicted Exposure Period Maps”, and “Reliability Maps” for easy comprehension. The observed exposure period at 5% exceedance probability (k5) was evaluated as the 95th percentile of observed exposure periods. Correct prediction implies that the predicted k5 is equal to the observed k5 for a particular month and location. Overprediction implies that the predicted exposure period is greater than the observed exposure period. Underprediction implies that the predicted exposure period is less than the observed exposure period. The reliability of each predicted exposure period was computed by drawing with replacement 10,000 samples of consecutive days equal to the predicted exposure period from the validation data and counting the number samples which contains at least one threshold day. A 95% chance of complete disinfection is guaranteed if the proportion of these samples with at least one threshold day is ≥ 0.95.太阳能消毒（SODIS）系统的运行所需曝露时长存在可变特性，其取决于多项工艺参数：云量、气温、水体浊度及病原体浓度。由曝露时长波动引发的不确定性，可通过概率方法予以消解。本研究提出一种从日照数据时间序列中提取曝露时长的概率化方法。为此，研究将曝露时长定义为连续曝露天数的累计值，直至出现太阳辐照度高于消毒阈值的当日为止。该定义与控制几何分布的底层物理过程相契合。若假设服从几何分布，则可针对任意地点，在给定超越概率下选取月度曝露时长的代表值。 3600条数据样本存放于名为"300个点位1-12月数据样本集"的文件夹中。该数据样本文件夹内的Excel工作簿，以数据所对应的纬度、经度及月份进行命名。"安德森-达兰拟合优度检验与模型验证结果"表格收录了针对不同点位与月份（300个点位×12个月）采集的3600条数据样本所开展的安德森-达兰拟合优度检验（Anderson-Darling Goodness-of-Fit Test）及模型验证的结果。上述验证结果还以地图形式分别呈现于《拟合优度地图》《曝露时长观测值与预测值对比地图》及《可靠性地图》中，以便于直观理解。 以5%超越概率下的观测曝露时长（k5）为例，其取值为观测曝露时长序列的第95百分位数。预测准确意味着，特定月份与点位下的预测k5与观测k5完全一致；预测偏高指预测曝露时长大于实际观测曝露时长；预测偏低则指预测曝露时长小于实际观测曝露时长。 各预测曝露时长的可靠性计算方式如下：从验证数据中有放回地抽取10000组与预测曝露时长相等的连续天数样本，统计其中至少包含1个阈值日的样本占比。若该占比≥0.95，则可保证达到95%的完全消毒可靠性。