write the blog post

docs/source/blog/posts/time-adapters.rst

 .. post:: 23 Nov, 2022
-    :tags: announcement, usage, v0.4
+    :tags: announcement, cookbook, usage, v0.4
     :category: How to
     :author: Martin Lange
     :excerpt: 1
+    :image: 1
 
-===============================================
-New time interpolation and integration adapters
-===============================================
+==================================
+Time interpolation and integration
+==================================
 
-Excerpt
+With version ``v0.4.0``, FINAM comes with a set of **new time interpolation and integration adapters**.
+In addition to the existing linear interpolation adapter,
+**step-wise interpolation** with a flexible step position is now available.
+Integration over the target component's time step supports averaging as well as **sum integration** (Area under Curve).
 
 ----
 
-Text
+In many FINAM coupling use cases, components will have different time steps.
+This requires ways to deal with data pulls that lie between push times,
+and with target time steps covering multiple source steps.
+
+FINAM provides several adapters for time interpolation and integration
+to provide the right method for a wide range of use cases.
+
+Time interpolation
+------------------
+
+Time interpolation is most useful for models with time steps of the same order of magnitude,
+or if the target time step is smaller than the source time step.
+
+Time interpolation adapters interpolate between the two adjacent data entries.
+In the illustration below, data entries are denoted by black circles.
+Interpolation results for linear and step-wise interpolation are shown as colored lines.
+
+.. plot:: api/plots/interpolation-methods.py
+
+    Illustration of interpolation methods.
+
+FINAM provides these time interpolation adapters:
+
+* :class:`.adapters.LinearTime` -- Linear time interpolation.
+* :class:`.adapters.StepTime` -- Step-wise time interpolation with adjustable step position.
+
+Time integration
+----------------
+
+Time integration is particularly useful in cases where the target has a much longer time step than the source.
+In these cases, interpolation would just provide a snapshot of the current data,
+but ignore the history over the longer time step.
+
+Further, sum integration (Area under Curve) allows to aggregate rate-like data (e.g. precipitation in *mm/d*)
+to amounts (e.g. total precipitation over the time step, in *mm*).
+
+Time integration adapters in FINAM keep track of pull events from the target,
+and aggregate data between the last and the current pull.
+This is illustrated in the figure below.
+
+.. plot:: api/plots/integration-methods.py
+
+    Illustration of time integration.
+
+.. note::
+    Time integration also requires an interpolation method.
+    The illustration uses linear interpolation, but step-wise interpolation is also supported
+    by all integration adapters.
+
+FINAM provides these time integration adapters:
+
+* :class:`.adapters.AvgOverTime` -- Time-weighted average integration.
+* :class:`.adapters.SumOverTime` -- Sum/Area under Curve integration.
+
+.. note::
+    The :class:`SumOverTime <.adapters.SumOverTime>` adapter may change units, depending on the setup.
+    This also allows to transform rates into amounts, like *mm/d* to total *mm*.