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Numerical models of Photodissociation Regions (PDRs) are an essential tool toquantitatively understand observations of massive star forming regions throughsimulations. Few mature PDR models are available and the Cologne KOSMA-$\tau$PDR model is the only sophisticated model that uses a spherical cloud geometrythereby allowing us to simulate clumpy PDRs. We present the current status ofthe code as reference for modelers and for observers that plan to applyKOSMA-$\tau$ to interpret their data. For the numerical solution of thechemical problem we present a superior Newton-Raphson stepping algorithm anddiscuss strategies to numerically stabilize the problem and speed up theiterations. The chemistry in KOSMA-$\tau$ is upgraded to include the fullsurface chemistry in an up-to-date formulation and we discuss a novelcomputation of branching ratios in chemical desorption reactions. The high dusttemperature in PDRs leads to a selective freeze-out of oxygen-bearing icespecies due to their higher condensation temperatures and we study changes inthe ice mantle structures depending on the PDR parameters, in particular theimpinging UV field. Selective freeze-out can produce enhanced C abundances andhigher gas temperatures resulting in a fine-structure line emission of atomiccarbon [C] enhanced by up to 50% if surface reactions are considered. We showhow recent ALMA observations of HCO$^+$ emission in the Orion Bar with highspatial resolution on the scale of individual clumps can be interpreted in thecontext of non-stationary, clumpy PDR ensembles. Additionally, we introduceWL-PDR, a simple plane-parallel PDR model written in Mathematica to act asnumerical testing environment of PDR modeling aspects.

The KOSMA-$\tau$ PDR Model -- I. Recent updates to the numerical model of photo-dissociated regions