Field contraction diagnostics

In EAMxx, we can automatically calculate field reductions across the horizontal columns and across the model vertical levels. We call these horizontal and vertical reductions. We can also automatically calculate zonal averages.

Horizontal reduction

We currently offer only one horizontal reduction \(C\), and it is defined as

\[ C_{\dots k} = \sum_{i} w_{i} \cdot F_{i \dots k} \]

where \(F_\text{i...k}\) is the field at column \(i\) and level \(k\), and \(w_{i}\) is the weight at column \(i\). We note that the field \(F\) can have other dimensions (\(\dots\)). The weight \(w\) is defined as the area fraction in column \(i\), that is, the area in column \(i\) divided by the total area in all columns.

To select the horizontal reduction, you only need to suffix a field name X with _horiz_avg in the output requests.

Reduction	Weight	Description
X_horiz_avg	Area fraction	Average across all columns

Vertical reduction

We currently offer three vertical reductions \(C\), defined as

\[ C_{\dots} = \sum_{k} w_{k} \cdot F_{\dots k} \]

where \(F_{\dots k}\) is the field at level \(k\), and \(w_{k}\) is the weight at level \(k\).

To select the vertical reduction, you only need to suffix a field name X with _vert_(avg|sum)_(dp|dz)_weighted or _vert_(avg|sum) in the output yaml files.

Reduction	Weight	Description
X_vert_avg_dp_weighted	\(\Delta p_{k}\)	Average across all levels, weighted by \(\Delta p_{k}\)
X_vert_sum_dp_weighted	\(\Delta p_{k}\)	Sum across all levels, weighted by \(\Delta p_{k}\)
X_vert_avg_dz_weighted	\(\Delta z_{k}\)	Average across all levels, weighted by \(\Delta z_{k}\)
X_vert_sum_dz_weighted	\(\Delta z_{k}\)	Sum across all levels, weighted by \(\Delta z_{k}\)
X_vert_avg	1	Average across all levels
X_vert_sum	1	Sum across all levels

The supported weighting options for now are

• pseudo_density field in EAMxx, \(\Delta p_{k}\), in units of Pa;
• dz field in EAMxx, \(\Delta z_{k}\), in units of m;
• and no weighting, which is equivalent to using a weight of 1.

In the case of pseudo_density, the weighting is scaled by 1/g, where g is the gravitational acceleration, in units of m/s\(^2\).

Zonal reduction

We currently have a utility to calculate zonal averages online. To select the zonal average, you need to suffix a field name X with _zonal_avg and the number of bins Y as _Y_bins. All zonal averages are calculated using the area fraction in each bin as the weight.

For 180 latitude bins, the bins are defined as follows: [-90, -89), [-89, -88), ..., [89, 90). For 90 latitude bins, the bins are defined as follows: [-90, -88), [-88, -86), ..., [88, 90). And so on...

Reduction	Weight	Description
X_zonal_avg_Y_bins	Area fraction	Average across the zonal direction

Example

%YAML 1.1
---
filename_prefix: monthly.outputs
averaging_type: average
max_snapshots_per_file: 1
fields:
  physics_pg2:
    field_names:
      # in this example, we use T_mid in units of K
      - T_mid_horiz_avg  # K
      - T_mid_vert_avg_dp_weighted  # K
      - T_mid_vert_sum_dp_weighted  # K * Pa * s / (m * m) 
      - T_mid_vert_avg_dz_weighted  # K
      - T_mid_vert_sum_dz_weighted  # K * m
      - T_mid_vert_avg  # K
      - T_mid_vert_sum  # K
      - T_mid_zonal_avg_180_bins  # K
      - T_mid_zonal_avg_90_bins  # K
output_control:
  frequency: 1
  frequency_units: nmonths