Data and code for "The Alpha-Omega Problem in the Assessments of Atmospheric Power"

OVERVIEW--------This archive contains the Wolfram Language scripts and processed numerical outputs usedfor the ERA5, JRA-3Q, and MERRA-2 calculations for calendar year 2025. The calculationsuse four analysis times per day (00, 06, 12, and 18 UTC), giving 1460 six-hourly samplesfor each reanalysis. The two diagnostics are: W_K horizontal pressure-gradient work / kinetic-energy generation W_omega pressure-coordinate alpha-omega diagnostic At each pressure level the scripts evaluate k = -u/(a cos(phi)) dPhi/dlambda - v/a dPhi/dphi and c = -omega alpha, alpha = Rd T (1 + 0.608 q)/p, and integrate the resulting quantities vertically with dp/g. Pressure levels below thelocal surface are excluded. Power values in the CSV files are in W m^-2 unless anotherunit is stated in the column name. ARCHIVE CONTENTS----------------code/ ERA5_power_KE_omega_full_resumable_6hourly_with_latitude_stencil.wl ERA5 calculation. JRA3Q_power_KE_omega_highres_resumable_6hourly_with_latitude_stencil_nonuniform.wl JRA-3Q calculation. The meridional derivative is evaluated on the supplied nonuniform Gaussian latitude grid, and Gaussian latitude weights are used for area integration. MERRA2_power_KE_omega_existing_daily_6hourly_v7_surface_stencil_with_latitude.wl MERRA-2 calculation from daily pressure-level files. The daily files contain 3-hourly fields; the script selects 00, 06, 12, and 18 UTC. results/ Five CSV products are supplied for each reanalysis: mean values, a 6-hourly time series, vertical profiles, latitude profiles, and pressure-level stencil diagnostics. RESULT FILES------------*_power_mean_2025_6hourly*.csv Time means over the 1460 processed analysis times. These files contain the global resolved diagnostics, surface-layer estimates and corresponding totals, and the resolved contributions below and above the 500-hPa layer-midpoint boundary. *_power_timeseries_2025_6hourly*.csv The same global diagnostics at every six-hourly analysis time. The "time" field uses YYYYMMDD_HHMM notation. *_power_vertical_profile_2025_6hourly*.csv Time-mean global contribution from each pressure layer. "layer_mid_hPa" is the midpoint pressure of the layer; "KE_layer_Wm2" and "omega_alpha_layer_Wm2" are the layer contributions to W_K and W_omega, respectively. Summing the layer values gives the corresponding resolved global diagnostic. *_power_latitude_profile_2025_6hourly*.csv Time-mean vertically integrated resolved diagnostics as zonal means versus latitude. "latitude_area_weight_fraction" gives the fraction of global surface area associated with each latitude row and sums to one. Area-weighting the zonal-mean profile with these fractions reproduces the corresponding resolved global mean. *_power_stencil_profile_2025_6hourly*.csv Time-mean pressure-level coverage of the horizontal derivative used for W_K: KE_center_valid_area_fraction global area fraction for which the central grid point is above the local surface and has valid input fields; KE_stencil_valid_area_fraction global area fraction for which the complete horizontal derivative stencil is valid; KE_stencil_retained_fraction_of_center stencil-valid area divided by center-valid area; KE_stencil_extra_area_loss_fraction center-valid area minus stencil-valid area. COLUMN-NAME CONVENTIONS-----------------------"KE_" denotes W_K and "omega_alpha_" denotes W_omega. "resolved" denotes the pressure-layer integral using only valid reanalysis levels. ForW_K, validity also requires the horizontal derivative stencil. "surface_*" denotes the estimated contribution between the local surface pressure andthe lowest valid pressure level. "total_*" is resolved plus that surface contribution. For ERA5 and JRA-3Q: "half" uses one half of the lowest valid level value across the unresolved surface pressure interval, equivalent to a linear decrease to zero at the surface; "extrap" linearly extrapolates from the two lowest valid levels when both are available, with the half estimate used as the fallback. For MERRA-2, three W_K surface sensitivities are included: "zero" value decreases linearly to zero at the surface; "constant" lowest valid level value is held constant to the surface; "extrap" value is linearly extrapolated from the two lowest valid levels. "lower_resolved" contains layers whose midpoint pressure is >= 500 hPa;"upper_resolved" is the remaining resolved contribution above this boundary. NUMERICAL DETAILS-----------------Horizontal longitude derivatives are periodic centered differences. ERA5 and MERRA-2use centered meridional differences away from the geographic poles; the pole rows arenot used for W_K. JRA-3Q uses a second-order derivative formula for the actual nonuniformGaussian latitude coordinates, with centered three-point differences in the interior andone-sided three-point differences at the two polewardmost Gaussian rows. The W_K derivative domain requires the central point and all points needed by thehorizontal derivative to be valid and above terrain. W_omega requires no horizontalstencil and therefore uses only the local validity and surface-pressure mask. Vertical layer integrals use trapezoidal averaging between adjacent valid pressurelevels. The supplied latitude and global means use spherical area weighting. JRA-3Q usesthe supplied Gaussian quadrature weights. ERA5 geopotential (z) is already Phi in m^2 s^-2 and is used directly. JRA-3Q h andMERRA-2 H are heights and are multiplied by g to obtain geopotential before horizontalderivatives are evaluated. SCRIPT STRUCTURE----------------Each script is self-contained and follows the same general sequence: 1. User settings: year, local data paths, months/days/times, output tag, and the 500-hPa lower/upper split. 2. Dataset variable names, physical constants, input cleaning, coordinate orientation, area weights, and finite/valid-data masks. 3. Horizontal derivative routines and W_K calculation, including the terrain stencil. 4. W_omega calculation from omega, temperature, humidity, and pressure. 5. Vertical integration, surface-layer estimates, lower/upper partition, and latitude and stencil diagnostics. 6. The time loop, which accumulates the mean profiles and writes the CSV products. The scripts support resuming an incomplete calculation. The scripts use Wolfram Language built-in import/export functionality and do not requireadditional Wolfram packages. RERUNNING THE CALCULATIONS--------------------------Raw ERA5, JRA-3Q, and MERRA-2 data are not included. To rerun a calculation, obtain thecorresponding reanalysis fields from the data provider and edit the local input and outputpaths in the "user settings" section near the beginning of the appropriate script. Theexpected input filenames and required variables are documented in the header of eachscript.