diff --git a/src/atlas/interpolation/method/structured/StructuredInterpolation2D.tcc b/src/atlas/interpolation/method/structured/StructuredInterpolation2D.tcc
index de71fb24c..2f2fa75a8 100644
--- a/src/atlas/interpolation/method/structured/StructuredInterpolation2D.tcc
+++ b/src/atlas/interpolation/method/structured/StructuredInterpolation2D.tcc
@@ -472,15 +472,24 @@ void StructuredInterpolation2D<Kernel>::do_execute( const FieldSet& src_fields,
     if ( datatype.kind() == array::DataType::KIND_REAL64 && rank == 1 ) {
         execute_impl<double, 1>( *kernel_, src_fields, tgt_fields );
     }
-    if ( datatype.kind() == array::DataType::KIND_REAL32 && rank == 1 ) {
+    else if ( datatype.kind() == array::DataType::KIND_REAL32 && rank == 1 ) {
         execute_impl<float, 1>( *kernel_, src_fields, tgt_fields );
     }
-    if ( datatype.kind() == array::DataType::KIND_REAL64 && rank == 2 ) {
+    else if ( datatype.kind() == array::DataType::KIND_REAL64 && rank == 2 ) {
         execute_impl<double, 2>( *kernel_, src_fields, tgt_fields );
     }
-    if ( datatype.kind() == array::DataType::KIND_REAL32 && rank == 2 ) {
+    else if ( datatype.kind() == array::DataType::KIND_REAL32 && rank == 2 ) {
         execute_impl<float, 2>( *kernel_, src_fields, tgt_fields );
     }
+    else if ( datatype.kind() == array::DataType::KIND_REAL64 && rank == 3 ) {
+        execute_impl<double, 3>( *kernel_, src_fields, tgt_fields );
+    }
+    else if ( datatype.kind() == array::DataType::KIND_REAL32 && rank == 3 ) {
+        execute_impl<float, 3>( *kernel_, src_fields, tgt_fields );
+    }
+    else {
+        ATLAS_NOTIMPLEMENTED;
+    }
 
     tgt_fields.set_dirty();
 }
diff --git a/src/atlas/interpolation/method/structured/kernels/CubicHorizontalKernel.h b/src/atlas/interpolation/method/structured/kernels/CubicHorizontalKernel.h
index 2d5fa016b..d4828e833 100644
--- a/src/atlas/interpolation/method/structured/kernels/CubicHorizontalKernel.h
+++ b/src/atlas/interpolation/method/structured/kernels/CubicHorizontalKernel.h
@@ -234,6 +234,39 @@ class CubicHorizontalKernel {
         }
     }
 
+    template <typename stencil_t, typename weights_t, typename Value, int Rank>
+    typename std::enable_if<(Rank == 3), void>::type interpolate(const stencil_t& stencil, const weights_t& weights,
+                                                                 const array::ArrayView<const Value, Rank>& input,
+                                                                 array::ArrayView<Value, Rank>& output, idx_t r) const {
+        std::array<std::array<idx_t, stencil_width()>, stencil_width()> index;
+        const auto& weights_j = weights.weights_j;
+        const idx_t Nk        = output.shape(1);
+        const idx_t Nl        = output.shape(2);
+
+        for (idx_t k = 0; k < Nk; ++k) {
+            for (idx_t l = 0; l < Nl; ++l) {
+                output(r, k, l) = 0.;
+            }
+        }
+        for (idx_t j = 0; j < stencil_width(); ++j) {
+            const auto& weights_i = weights.weights_i[j];
+            for (idx_t i = 0; i < stencil_width(); ++i) {
+                idx_t n = src_.index(stencil.i(i, j), stencil.j(j));
+                Value w = static_cast<Value>(weights_i[i] * weights_j[j]);
+                for (idx_t k = 0; k < Nk; ++k) {
+                    for (idx_t l = 0; l < Nl; ++l) {
+                        output(r, k, l) += w * input(n, k, l);
+                    }
+                }
+                index[j][i] = n;
+            }
+        }
+
+        if (limiter_) {
+            Limiter::limit(index, input, output, r);
+        }
+    }
+
     template <typename array_t>
     typename array_t::value_type operator()(double x, double y, const array_t& input) const {
         Stencil stencil;
diff --git a/src/atlas/interpolation/method/structured/kernels/CubicHorizontalLimiter.h b/src/atlas/interpolation/method/structured/kernels/CubicHorizontalLimiter.h
index 04fecd246..75371985b 100644
--- a/src/atlas/interpolation/method/structured/kernels/CubicHorizontalLimiter.h
+++ b/src/atlas/interpolation/method/structured/kernels/CubicHorizontalLimiter.h
@@ -108,6 +108,39 @@ class CubicHorizontalLimiter {
             }
         }
     }
+
+    template <typename Value, int Rank>
+    static typename std::enable_if<(Rank == 3), void>::type limit(const std::array<std::array<idx_t, 4>, 4>& index,
+                                                                  const array::ArrayView<const Value, Rank>& input,
+                                                                  array::ArrayView<Value, Rank>& output, idx_t r) {
+        // Limit output to max/min of values in stencil marked by '*'
+        //         x        x        x         x
+        //              x     *-----*     x
+        //                   /   P  |
+        //          x       *------ *        x
+        //        x        x        x         x
+        for (idx_t k = 0; k < output.shape(1); ++k) {
+            for (idx_t l = 0; l < output.shape(2); ++l) {
+                Value maxval = std::numeric_limits<Value>::lowest();
+                Value minval = std::numeric_limits<Value>::max();
+                for (idx_t j = 1; j < 3; ++j) {
+                    for (idx_t i = 1; i < 3; ++i) {
+                        idx_t n   = index[j][i];
+                        Value val = input(n, k, l);
+                        maxval    = std::max(maxval, val);
+                        minval    = std::min(minval, val);
+                    }
+                }
+                if (output(r, k, l) < minval) {
+                    output(r, k, l) = minval;
+                }
+                else if (output(r, k, l) > maxval) {
+                    output(r, k, l) = maxval;
+                }
+            }
+        }
+    }
+
 };
 
 }  // namespace method
diff --git a/src/atlas/interpolation/method/structured/kernels/LinearHorizontalKernel.h b/src/atlas/interpolation/method/structured/kernels/LinearHorizontalKernel.h
index d0815c7c2..c4298c5ae 100644
--- a/src/atlas/interpolation/method/structured/kernels/LinearHorizontalKernel.h
+++ b/src/atlas/interpolation/method/structured/kernels/LinearHorizontalKernel.h
@@ -186,6 +186,32 @@ class LinearHorizontalKernel {
         }
     }
 
+    template <typename stencil_t, typename weights_t, typename Value, int Rank>
+    typename std::enable_if<(Rank == 3), void>::type interpolate(const stencil_t& stencil, const weights_t& weights,
+                                                                 const array::ArrayView<const Value, Rank>& input,
+                                                                 array::ArrayView<Value, Rank>& output, idx_t r) const {
+        const auto& weights_j = weights.weights_j;
+        const idx_t Nk        = output.shape(1);
+        const idx_t Nl        = output.shape(2);
+        for (idx_t k = 0; k < Nk; ++k) {
+            for (idx_t l = 0; l < Nl; ++l) {
+                output(r, k, l) = 0.;
+            }
+        }
+        for (idx_t j = 0; j < stencil_width(); ++j) {
+            const auto& weights_i = weights.weights_i[j];
+            for (idx_t i = 0; i < stencil_width(); ++i) {
+                idx_t n = src_.index(stencil.i(i, j), stencil.j(j));
+                Value w = static_cast<Value>(weights_i[i] * weights_j[j]);
+                for (idx_t k = 0; k < Nk; ++k) {
+                    for (idx_t l = 0; l < Nl; ++l) {
+                        output(r, k, l) += w * input(n, k, l);
+                    }
+                }
+            }
+        }
+    }
+
     template <typename array_t>
     typename array_t::value_type operator()(double x, double y, const array_t& input) const {
         Stencil stencil;
diff --git a/src/atlas/interpolation/method/structured/kernels/QuasiCubicHorizontalKernel.h b/src/atlas/interpolation/method/structured/kernels/QuasiCubicHorizontalKernel.h
index 463cb9765..54777e7b9 100644
--- a/src/atlas/interpolation/method/structured/kernels/QuasiCubicHorizontalKernel.h
+++ b/src/atlas/interpolation/method/structured/kernels/QuasiCubicHorizontalKernel.h
@@ -285,6 +285,57 @@ class QuasiCubicHorizontalKernel {
         }
     }
 
+
+    template <typename stencil_t, typename weights_t, typename Value, int Rank>
+    typename std::enable_if<(Rank == 3), void>::type interpolate(const stencil_t& stencil, const weights_t& weights,
+                                                                 const array::ArrayView<const Value, Rank>& input,
+                                                                 array::ArrayView<Value, Rank>& output, idx_t r) const {
+        std::array<std::array<idx_t, stencil_width()>, stencil_width()> index;
+        const auto& weights_j = weights.weights_j;
+        const idx_t Nk        = output.shape(1);
+        const idx_t Nl        = output.shape(2);
+        for (idx_t k = 0; k < Nk; ++k) {
+            for (idx_t l = 0; l < Nl; ++l) {
+                output(r, k, l) = 0.;
+            }
+        }
+
+        // LINEAR for outer rows  ( j = {0,3} )
+        for (idx_t j = 0; j < 4; j += 3) {
+            const auto& weights_i = weights.weights_i[j];
+            for (idx_t i = 1; i < 3; ++i) {  // i = {1,2}
+                idx_t n = src_.index(stencil.i(i, j), stencil.j(j));
+                Value w = weights_i[i] * weights_j[j];
+                for (idx_t k = 0; k < Nk; ++k) {
+                    for (idx_t l = 0; l < Nl; ++l) {
+                        output(r, k, l) += w * input(n, k, l);
+                    }
+                }
+                index[j][i] = n;
+            }
+        }
+        // CUBIC for inner rows ( j = {1,2} )
+        for (idx_t j = 1; j < 3; ++j) {
+            const auto& weights_i = weights.weights_i[j];
+            for (idx_t i = 0; i < stencil_width(); ++i) {
+                idx_t n = src_.index(stencil.i(i, j), stencil.j(j));
+                Value w = weights_i[i] * weights_j[j];
+                for (idx_t k = 0; k < Nk; ++k) {
+                    for (idx_t l = 0; l < Nl; ++l) {
+                        output(r, k, l) += w * input(n, k, l);
+                    }
+                }
+                index[j][i] = n;
+            }
+        }
+
+        if (limiter_) {
+            Limiter::limit(index, input, output, r);
+        }
+    }
+
+
+
     template <typename array_t>
     typename array_t::value_type operator()(double x, double y, const array_t& input) const {
         Stencil stencil;