diff --git a/src/anemoi/models/layers/bounding.py b/src/anemoi/models/layers/bounding.py
index b168591d..c0e8e459 100644
--- a/src/anemoi/models/layers/bounding.py
+++ b/src/anemoi/models/layers/bounding.py
@@ -11,6 +11,7 @@
 
 from abc import ABC
 from abc import abstractmethod
+from typing import Optional
 
 import torch
 from torch import nn
@@ -30,12 +31,28 @@ def __init__(
         *,
         variables: list[str],
         name_to_index: dict,
+        statistics: Optional[dict] = None,
+        name_to_index_stats: Optional[dict] = None,
     ) -> None:
+        """Initializes the bounding strategy.
+        Parameters
+        ----------
+        variables : list[str]
+            A list of strings representing the variables that will be bounded.
+        name_to_index : dict
+            A dictionary mapping the variable names to their corresponding indices.
+        statistics : dict, optional
+            A dictionary containing the statistics of the variables.
+        name_to_index_stats : dict, optional
+            A dictionary mapping the variable names to their corresponding indices in the statistics dictionary
+        """
         super().__init__()
 
         self.name_to_index = name_to_index
         self.variables = variables
         self.data_index = self._create_index(variables=self.variables)
+        self.statistics = statistics
+        self.name_to_index_stats = name_to_index_stats
 
     def _create_index(self, variables: list[str]) -> InputTensorIndex:
         return InputTensorIndex(includes=variables, excludes=[], name_to_index=self.name_to_index)._only
@@ -63,7 +80,92 @@ class ReluBounding(BaseBounding):
     def forward(self, x: torch.Tensor) -> torch.Tensor:
         x[..., self.data_index] = torch.nn.functional.relu(x[..., self.data_index])
         return x
+    
+
+class NormalizedReluBounding(BaseBounding):
+    """Bounding variable with a ReLU activation and customizable normalized thresholds."""
 
+    def __init__(
+        self,
+        *,
+        variables: list[str],
+        name_to_index: dict,
+        min_val: list[float],
+        normalizer: list[str],
+        statistics: dict,
+        name_to_index_stats: dict,
+    ) -> None:
+        """Initializes the NormalizedReluBounding with the specified parameters.
+
+        Parameters
+        ----------
+        variables : list[str]
+            A list of strings representing the variables that will be bounded.
+        name_to_index : dict
+            A dictionary mapping the variable names to their corresponding indices.
+        statistics : dict
+            A dictionary containing the statistics of the variables (mean, std, min, max, etc.).
+        min_val : list[float]
+            The minimum values for the ReLU activation. It should be given in the same order as the variables.
+        normalizer : list[str]
+            A list of normalization types to apply, one per variable. Options: 'mean-std', 'min-max', 'max', 'std'.
+        name_to_index_stats : dict
+            A dictionary mapping the variable names to their corresponding indices in the statistics dictionary.
+        """
+        super().__init__(
+            variables=variables,
+            name_to_index=name_to_index,
+            statistics=statistics,
+            name_to_index_stats=name_to_index_stats,
+        )
+        self.min_val = min_val
+        self.normalizer = normalizer
+
+        # Validate normalizer input
+        if not all(norm in {"mean-std", "min-max", "max", "std"} for norm in self.normalizer):
+            raise ValueError("Each normalizer must be one of: 'mean-std', 'min-max', 'max', 'std' in NormalizedReluBounding.")
+        if len(self.normalizer) != len(variables):
+            raise ValueError("The length of the normalizer list must match the number of variables in NormalizedReluBounding.")
+        if len(self.min_val) != len(variables):
+            raise ValueError("The length of the min_val list must match the number of variables in NormalizedReluBounding.")
+
+        self.norm_min_val = torch.zeros(len(variables))
+        for ii, variable in enumerate(variables):
+            stat_index = self.name_to_index_stats[variable]
+            if self.normalizer[ii] == "mean-std":
+                mean = self.statistics["mean"][stat_index]
+                std = self.statistics["stdev"][stat_index]
+                self.norm_min_val[ii] = (min_val[ii] - mean) / std
+            elif self.normalizer[ii] == "min-max":
+                min_stat = self.statistics["min"][stat_index]
+                max_stat = self.statistics["max"][stat_index]
+                self.norm_min_val[ii] = (min_val[ii] - min_stat) / (max_stat - min_stat)
+            elif self.normalizer[ii] == "max":
+                max_stat = self.statistics["max"][stat_index]
+                self.norm_min_val[ii] = min_val[ii] / max_stat
+            elif self.normalizer[ii] == "std":
+                std = self.statistics["stdev"][stat_index]
+                self.norm_min_val[ii] = min_val[ii] / std
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        """Applies the ReLU activation with the normalized minimum values to the input tensor.
+
+        Parameters
+        ----------
+        x : torch.Tensor
+            The input tensor to process.
+
+        Returns
+        -------
+        torch.Tensor
+            The processed tensor with bounding applied.
+        """
+        self.norm_min_val = self.norm_min_val.to(x.device)
+        x[..., self.data_index] = (
+            torch.nn.functional.relu(x[..., self.data_index] - self.norm_min_val)
+            + self.norm_min_val
+        )
+        return x
 
 class HardtanhBounding(BaseBounding):
     """Initializes the bounding with specified minimum and maximum values for bounding.