The recent development of successful model approaches that predict the photochemical behaviour of surface waters has greatly aided in the understanding of how water environments work and will likely work in the future, from a photochemical point of view. However, the inherent multi-wavelength (polychromatic) nature of environmental photochemistry causes the relevant mathematics to be quite complex, which discourages many scientists to carry out photochemical calculations. To greatly simplify model mathematics, this paper proposes a new approach that is based on a monochromatic approximation to the polychromatic problem, introducing the concept of what is here defined as equivalent monochromatic wavelengths (EMWs). The EMW is the single wavelength that reproduces the behaviour of the polychromatic system, using a monochromatic (Lambert-Beer based) equation. The EMW approach largely simplifies calculations, getting rid of integrals and allowing for much more straightforward and manageable equations to be obtained. In particular, this work shows that: (i) the EMW approach, although approximated, entails a negligible loss in accuracy compared to the exact polychromatic treatment of photochemical reactions; (ii) in the case of direct photolysis, the quantum yield is to be replaced by an apparent photon efficiency that is not bound to be < 1 (quantum yields can actually be > 1 for chain reactions and few other cases, but this is not the point here); (iii) the monochromatic Lambert-Beer equations work in most cases once the EMW is identified, with the present exception of sunlight absorption by chromophoric dissolved organic matter (CDOM). The latter spans a very wide wavelength range (from 300 to at least 600 nm), which makes a single-wavelength treatment more difficult. However, a relatively small modification to the monochromatic Lambert-Beer equation allows for successfully using the EMW approach, in the case of CDOM as well. The near-perfect coincidence between polychromatic and EMW-based predictions of photodegradation kinetics is here shown for the pollutants atrazine, bentazone, carbamazepine, diclofenac, diuron and ibuprofen. Extension to additional compounds requires translation of the traditional, polychromatic language into the EMW one. Hopefully, this contribution will introduce a new paradigm in the mathematical description of photochemical reactions in environmental waters. It could also become a new and simple way to treat multi-wavelength systems in general photochemistry studies, thereby completely changing the way multi-wavelength problems are dealt with.

从光化学的观点来看，预测地表水的光化学行为的成功模型方法的最新发展极大地帮助了人们了解水环境如何工作以及将来可能会如何工作。但是，环境光化学固有的多波长（多色）性质导致数学非常复杂，并且使许多科学家不愿进行光化学计算。为了大大简化模型数学，本文提出了一种基于单色逼近多色问题的新方法，并引入了所谓的等效单色波长（EMW）的概念。EMW是再现多色系统行为的单个波长，使用单色（基于Lambert-Beer的）方程式。EMW方法在很大程度上简化了计算，摆脱了积分，并允许获得更加直接和易于管理的方程式。尤其是，这项工作表明：（i） EMW方法虽然近似，但与光化学反应的精确多色处理相比，准确性损失可忽略不计；（ii）在直接光解的情况下，量子产率将被表观光子效率所取代，该表观光子效率不必然小于1（对于链式反应和其他少数情况，量子产率实际上可能大于1），但这不是这里的重点）；（iii）一旦确定了EMW，单色Lambert-Beer方程在大多数情况下都会起作用，但目前有色溶解有机物（CDOM）吸收阳光。后者跨越非常宽的波长范围（从300到至少600 nm），这使得单波长处理更加困难。但是，对单色Lambert-Beer方程的较小修改也可以在CDOM的情况下成功使用EMW方法。对于污染物阿特拉津，苯达松，卡马西平，双氯芬酸，双嘧磺隆和布洛芬，在多色和基于EMW的光降解动力学预测之间几乎完全吻合。要扩展其他化合物，需要将传统的多色语言翻译成EMW语言。希望，这一贡献将为环境水域中光化学反应的数学描述引入新的范例。它也可能成为常规光化学研究中处理多波长系统的一种新的简单方法，从而完全改变了解决多波长问题的方式。