diff --git a/src/anemoi/transform/fields.py b/src/anemoi/transform/fields.py
index 8bdbb161..ab7facbf 100644
--- a/src/anemoi/transform/fields.py
+++ b/src/anemoi/transform/fields.py
@@ -698,6 +698,24 @@ def new_field_with_metadata(template: WrappedField, **metadata: Any) -> NewMetad
     return NewMetadataField(template, **metadata)
 
 
+def new_field_with_units(template: WrappedField, units: str) -> NewMetadataField:
+    """Create a new field with units.
+
+    Parameters
+    ----------
+    template : WrappedField
+        The template field to use.
+    units : str
+        The units for the new field.
+
+    Returns
+    -------
+    NewMetadataField
+        The new field with the provided units.
+    """
+    return NewMetadataField(template, units=units)
+
+
 def new_field_from_latitudes_longitudes(
     template: WrappedField, latitudes: np.ndarray, longitudes: np.ndarray
 ) -> NewLatLonField:
diff --git a/src/anemoi/transform/filters/fields/glacier_mask.py b/src/anemoi/transform/filters/fields/glacier_mask.py
index ba0fec48..2ce60bed 100644
--- a/src/anemoi/transform/filters/fields/glacier_mask.py
+++ b/src/anemoi/transform/filters/fields/glacier_mask.py
@@ -62,4 +62,6 @@ def forward_transform(self, snow_depth: ekd.Field) -> ekd.Field:
         """
         snow_depth_masked = mask_glaciers(snow_depth.to_numpy(), self.glacier_mask)
 
-        return self.new_field_from_numpy(snow_depth_masked, template=snow_depth, param=self.snow_depth_masked)
+        return self.new_field_from_numpy(
+            snow_depth_masked, template=snow_depth, param=self.snow_depth_masked, units="Fraction"
+        )
diff --git a/src/anemoi/transform/filters/fields/matching.py b/src/anemoi/transform/filters/fields/matching.py
index 699f5eb0..5fdb2499 100644
--- a/src/anemoi/transform/filters/fields/matching.py
+++ b/src/anemoi/transform/filters/fields/matching.py
@@ -360,7 +360,7 @@ def _transform(
                 result.append(f)
         return self.new_fieldlist_from_list(result)
 
-    def new_field_from_numpy(self, array: np.ndarray, *, template: ekd.Field, param: str) -> ekd.Field:
+    def new_field_from_numpy(self, array: np.ndarray, *, template: ekd.Field, **kwargs) -> ekd.Field:
         """Create a new field from a numpy array.
 
         Parameters
@@ -369,15 +369,15 @@ def new_field_from_numpy(self, array: np.ndarray, *, template: ekd.Field, param:
             Numpy array containing the field data.
         template : ekd.Field
             Template field to use for metadata.
-        param : str
-            Parameter name for the new field.
+        **kwargs : Any
+            Additional keyword arguments for the new field.
 
         Returns
         -------
         ekd.Field
             New field created from the numpy array.
         """
-        return new_field_from_numpy(array, template=template, param=param)
+        return new_field_from_numpy(array, template=template, **kwargs)
 
     def new_fieldlist_from_list(self, fields: list[ekd.Field]) -> ekd.FieldList:
         """Create a new field list from a list of fields.
diff --git a/src/anemoi/transform/filters/fields/rescale.py b/src/anemoi/transform/filters/fields/rescale.py
index 91d5584a..65f81aae 100644
--- a/src/anemoi/transform/filters/fields/rescale.py
+++ b/src/anemoi/transform/filters/fields/rescale.py
@@ -36,6 +36,9 @@ class RescaleMixin(ABC):
     # intended to be inherited from SingleFieldFilter
     new_field_from_numpy: Callable
 
+    forward_units = None
+    backward_units = None
+
     @abstractmethod
     def prepare_filter(self):
         raise NotImplementedError("prepare_filter must be implemented by subclasses.")
@@ -46,7 +49,7 @@ def forward_select(self):
     def forward_transform(self, param: ekd.Field) -> ekd.Field:
         """Apply the forward transformation (x to ax+b)."""
         rescaled = self.rescaler.forward(param.to_numpy())
-        return self.new_field_from_numpy(rescaled, template=param, param=self.param)
+        return self.new_field_from_numpy(rescaled, template=param, param=self.param, units=self.forward_units)
 
     def backward_transform(self, param: ekd.Field) -> ekd.Field:
         """Apply the backward transformation (ax+b to x)."""
@@ -66,8 +69,7 @@ def prepare_filter(self):
 class Convert(RescaleMixin, SingleFieldFilter):
     """A filter to convert a parameter in a given unit to another unit, and back.
 
-    This filter uses :mod:`cfunits` (see the `cfunits documentation <https://ncas-cms.github.io/cfunits/>`_)
-    to compute the scale and offset.
+    This filter uses :mod:`pint` to compute the scale and offset.
 
     Examples
     --------
@@ -89,12 +91,16 @@ class Convert(RescaleMixin, SingleFieldFilter):
     required_inputs = ("unit_in", "unit_out", "param")
 
     def prepare_filter(self):
-        from cfunits import Units
+        import pint
+
+        ureg = pint.UnitRegistry()
+
+        self.forward_units = self.unit_out
+        self.backward_units = self.unit_in
 
-        u0 = Units(self.unit_in)
-        u1 = Units(self.unit_out)
         x1, x2 = 0.0, 1.0
-        y1, y2 = Units.conform([x1, x2], u0, u1)
+        y1 = ureg.Quantity(x1, self.unit_in).to(self.unit_out).magnitude
+        y2 = ureg.Quantity(x2, self.unit_in).to(self.unit_out).magnitude
         scale = (y2 - y1) / (x2 - x1)
         offset = y1 - scale * x1
 
diff --git a/src/anemoi/transform/filters/fields/snow_cover.py b/src/anemoi/transform/filters/fields/snow_cover.py
index b38e256a..a2ac83f7 100644
--- a/src/anemoi/transform/filters/fields/snow_cover.py
+++ b/src/anemoi/transform/filters/fields/snow_cover.py
@@ -119,4 +119,4 @@ def forward_transform(self, snow_depth: ekd.Field, snow_density: ekd.Field) -> I
         """
         snow_cover = compute_snow_cover(snow_depth.to_numpy(), snow_density.to_numpy())
 
-        yield self.new_field_from_numpy(snow_cover, template=snow_depth, param=self.snow_cover)
+        yield self.new_field_from_numpy(snow_cover, template=snow_depth, param=self.snow_cover, units="Fraction")
diff --git a/src/anemoi/transform/units.py b/src/anemoi/transform/units.py
new file mode 100644
index 00000000..d3ce9528
--- /dev/null
+++ b/src/anemoi/transform/units.py
@@ -0,0 +1,39 @@
+# (C) Copyright 2026 Anemoi contributors.
+#
+# This software is licensed under the terms of the Apache Licence Version 2.0
+# which can be obtained at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# In applying this licence, ECMWF does not waive the privileges and immunities
+# granted to it by virtue of its status as an intergovernmental organisation
+# nor does it submit to any jurisdiction.
+
+UNITS_MAPPING = {
+    "Numeric": "dimensionless",  # This is WMO, but Numeric will choke pint or cfunits
+}
+
+
+class Units:
+    def __init__(self, units: str) -> None:
+        self.units = units
+
+    def __str__(self) -> str:
+        return self.units
+
+    def __repr__(self) -> str:
+        return self.units
+
+    def __eq__(self, value):
+        if isinstance(value, Units):
+            return self.units == value.units
+        elif isinstance(value, str):
+            return self.units == value
+        else:
+            return NotImplemented
+
+    def __hash__(self):
+        return hash(self.units)
+
+    @classmethod
+    def to_canonical(cls, units: str) -> str:
+        """Converts a unit to its canonical form."""
+        return UNITS_MAPPING.get(units, units)
diff --git a/src/anemoi/transform/variables/__init__.py b/src/anemoi/transform/variables/__init__.py
index 4fe41e3a..8dc147fe 100644
--- a/src/anemoi/transform/variables/__init__.py
+++ b/src/anemoi/transform/variables/__init__.py
@@ -7,6 +7,7 @@
 # granted to it by virtue of its status as an intergovernmental organisation
 # nor does it submit to any jurisdiction.
 
+import logging
 from abc import ABC
 from abc import abstractmethod
 from typing import TYPE_CHECKING
@@ -16,6 +17,8 @@
 if TYPE_CHECKING:
     from datetime import timedelta
 
+LOG = logging.getLogger(__name__)
+
 
 class Variable(ABC):
     """Variable is a class that represents a variable during
@@ -191,6 +194,12 @@ def is_from_input(self) -> bool:
         """Check if the variable is from input."""
         pass
 
+    @property
+    @abstractmethod
+    def units(self):
+        """Get the units of the variable."""
+        pass
+
     def similarity(self, other: Any) -> int:
         """Compute the similarity between two variables. This is used when
         encoding a variable in GRIB and we do not have a template for it.
@@ -207,3 +216,58 @@ def similarity(self, other: Any) -> int:
             The similarity score.
         """
         return 0
+
+    def compatible(self, other: Any, return_reason: bool = False, **options) -> bool:
+        if options is None:
+            options = {}
+
+        def _compare():
+
+            if self.units != other.units:
+                if self.units is None or other.units is None:
+                    LOG.warning(
+                        f"{self}: one of the variables has missing units: {self.units} vs {other.units}. Assuming they are compatible."
+                    )
+                else:
+                    return f"Units are not compatible: {self.units} vs {other.units}"
+
+            if self.time_processing != other.time_processing:
+                return f"Time processinging types are not compatible: {self.time_processing} vs {other.time_processing}"
+
+            if self.period != other.period:
+                return f"Periods are not compatible: {self.period} vs {other.period}"
+
+            if self.is_pressure_level != other.is_pressure_level:
+                return f"Pressure level status is not compatible: {self.is_pressure_level} vs {other.is_pressure_level}"
+
+            if self.is_model_level != other.is_model_level:
+                return f"Model level status is not compatible: {self.is_model_level} vs {other.is_model_level}"
+
+            if self.is_surface_level != other.is_surface_level:
+                return f"Surface level status is not compatible: {self.is_surface_level} vs {other.is_surface_level}"
+
+        reason = _compare()
+        if reason:
+            return False, reason if return_reason else False
+
+        return True, None if return_reason else True
+
+    @classmethod
+    def check_compatibility(cls, variables1: dict, variables2: dict, **options) -> bool:
+        if options is None:
+            options = {}
+
+        keys1 = set(variables1.keys())
+        keys2 = set(variables2.keys())
+
+        if keys1 != keys2:
+            raise ValueError(f"Variable compatibility: missing={keys1-keys2}, added={keys2-keys1}")
+
+        reasons = []
+        for k in keys1:
+            compatible, reason = variables1[k].compatible(variables2[k], return_reason=True, **options)
+            if not compatible:
+                reasons.append(f"{k}: {reason}")
+
+        if reasons:
+            raise ValueError(f"Variables are not compatible: {'; '.join(reasons)}")
diff --git a/src/anemoi/transform/variables/variables.py b/src/anemoi/transform/variables/variables.py
index cf96e4d2..3ae1b6c5 100644
--- a/src/anemoi/transform/variables/variables.py
+++ b/src/anemoi/transform/variables/variables.py
@@ -15,6 +15,7 @@
 
 from anemoi.utils.dates import as_timedelta
 
+from anemoi.transform.units import Units
 from anemoi.transform.variables import Variable
 
 if TYPE_CHECKING:
@@ -106,6 +107,11 @@ def period(self) -> Union["timedelta", None]:
 
         return as_timedelta(period[1]) - as_timedelta(period[0])
 
+    @property
+    def units(self):
+        units = self.data.get("units", None)
+        return Units(units) if units else None
+
     @property
     def grib_keys(self) -> dict[str, Any]:
         """Get the GRIB keys of the variable."""
diff --git a/tests/field_filters/test_rescale.py b/tests/field_filters/test_rescale.py
index 0d6e9cda..e273d1bd 100644
--- a/tests/field_filters/test_rescale.py
+++ b/tests/field_filters/test_rescale.py
@@ -9,25 +9,11 @@
 
 import earthkit.data as ekd
 import numpy.testing as npt
-import pytest
 from anemoi.utils.testing import skip_if_offline
 
 from anemoi.transform.filters import create_filter_by_name as create_filter
 
 
-def skip_missing_udunits2():
-    """Skip tests if udunits2 package is not available."""
-    # Can't use utils.testing.skip_missing_packages because it only fails
-    # when cfunits.Units is imported...
-    # NB: cfunits depends on udunits2 which is a system library and not installed with pip
-    try:
-        from cfunits import Units  # noqa: F401
-
-        return lambda f: f
-    except FileNotFoundError:
-        return pytest.mark.skip(reason="udunits2 not found")
-
-
 @skip_if_offline
 def test_rescale(fieldlist: ekd.FieldList) -> None:
     """Test rescaling temperature from Kelvin to Celsius and back.
@@ -58,7 +44,6 @@ def test_rescale(fieldlist: ekd.FieldList) -> None:
             npt.assert_allclose(before_filter[param], after_forward[param])
 
 
-@skip_missing_udunits2()
 @skip_if_offline
 def test_convert(fieldlist: ekd.FieldList) -> None:
     """Test converting temperature from Kelvin to Celsius and back.