Update README.md

README.md

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 license: apache-2.0
 ---
 
-% Data format description for the nonlocal gravity wave parameterization dataset
+<h1>Data format description for the nonlocal gravity wave parameterization dataset</h1>
 
-% Contact: https://github.com/amangupta2 or amangupta2@gmail.com
+<h1>Data Source</h1>
 
-% Date: 19 September 2024
+The dataset contains input and output training pairs computed using ECMWF's ERA5. The dataset was computed for the years 2010, 2012, 2014, and 2015. One month (from the validation set) is provided here for testing. 
 
-The nonlocal parameterization dataset contains input features for the background atmospheric field and output labels for the subgrid-scale fluxes for those fields computed using ECMWF's ERA5. The full dataset comprises atmospheric state and fluxes computed for the years 2010, 2012, 2014, and 2015. Out of the 48 months computed, one (from the validation set) is provided here for testing. 
+<h1>Variables Description</h1>
 
-The SCIENCE GOAL is to learn small-scale dynamics from high-resolution models/datasets (ERA5, which can resolve those dynamics) and couple it back to a coarse-resolution climate model (which cannot resolve those dynamics) to represent the missing physics. Typically this is done through crude physical parameterizations. The focus is on one such gray-zone process - atmospheric gravity waves. Gravity wave parameterizations guess the momentum fluxes from the background state and other surface tensors. The forcing corresponding to the predicted fluxes is coupled back to the momentum tendencies in the dynamical core. Helmholtz decomposition is used to extract the gravity wave momentum fluxes from raw ERA5 data on model levels. This data is used for fine-tuning. The data is "conservatively" coarsegrained from the ERA5 25 km grid to a coarse ~300 km 64x128 Gaussian grid because (a) the coarse-climate model only resolves the large-scale coarsegrain winds. The coarse winds will be used to invoke the coupled ML models, and (b) The wave fluxes, i.e. the true momentum flux is defined by averaging over the whole wave cycle. Thus, it is important to average the fluxes over the largest resolved wavenumber associated with gravity waves to get a true measure of the fluxes and prevent wavy phase-dependent artifacts in the flux computations. 
+1. Dimensional variables: 64 latitudes (LAT) and 128 longitudes (LON)
+2. features: background atmospheric state, fixed surface variables lat, lon, surface elevation and \\(u, v, T, P\\), concatenated along the vertical dimension. 
+3. output: potential temperature \\(\theta \\) and momentum fluxes, \\(u'\omega',v'\omega'\\), concatenated along the vertical dimension.
 
-The netCDF file contains:
+<h1>Variables Shape</h1>
+1. Input shape: TIME x IDIM x LAT x LON<br />
+2. Output shape: TIME x ODIM x LAT x LON<br />
 
-dimensional variables: 64 latitudes (LAT) and 128 longitudes (LON)
-features: input features, i.e., the background state of the atmosphere, with dimension TIME x IDIM x LAT x LON
-output: output fluxes, i.e., the momentum fluxes carried by the gravity waves, computed using Helmholtz Decomposition, for the background state, with dimension TIME x ODIM x LAT x LON
-IDIM = 491, ODIM = 366
+Here, IDIM = 491, ODIM = 366, LAT=64, LON=128, TIME index ranges from 0 to 24*31 for months wth 31 days
 
-The input (features) has a vertical dimension (IDIM) equal to 491 (3 + 4x122) because it is created by concatenating the latitude (1), longitude (1), surface elevation (1), zonal winds (122), meridional winds (122), temperature (122), and pressure (122), along the vertical dimension. Thus, IDIM index 0 corresponds to latitude, 1 corresponds to longitude, 2 corresponds to surface elevation for the given latitude and longitude, 3 to 124 correspond to zonal wind, 125 to 246 correspond to meridional wind, 247 to 368 correspond to temperature, and 369 to 490 correspond to pressure.
+<center>
+<img src="https://huggingface.co/datasets/Prithvi-WxC/Gravity_wave_Parameterization/resolve/main/prithvi_schematic.png" alt="Gravity Wave" width="60%"/>
+</center>
 
-Likewise, the output has a vertical dimension (ODIM) equal to 366 (3x122) because it is created by concatenating the potential temperature (122), zonal flux of vertical momentum (122) and the meridional flux of vertical momentum (122) along the vertical dimension. ODIM 0 to 121 correspond to the potential temperature, ODIM 122 to 243 correspond to the zonal flux component, and ODIM 244 to 365 correspond to the meridional flux component.
+<h1>Variables Indices</h1>
 
-Therefore, the neural network would predict the potential temperature, zonal and meridional momentum fluxes on 122 pressure level each, using the latitude, longitude, and surface elevation, and the zonal wind, meridional wind, and potential temperature on 122 pressure levels. The main prediction task is to predict the momentum fluxes, but since the potential temperature is a nonlinear function of temperature and pressure, having it as an output allows testing the capability of the model to predict simpler analytical relationships to assess model performance.
+<b>Input:</b> has IDIM=491 (3 + 4x122) channels. It is created by concatenating the latitude (1), longitude (1), surface elevation (1), zonal winds \\(u\\) (122), meridional winds \\(v\\) (122), temperature \\(T\\) (122), and pressure \\(P\\) (122), along the vertical dimension. IDIM index 0 corresponds to latitude, 1 corresponds to longitude, 2 corresponds to surface elevation for the given latitude and longitude, 3 to 124 correspond to zonal wind, and so on.
 
-The netCDF attributes described the scaling recipe for each variable. To view, execute: ncdump -h <filename>
+<b>Output:</b> has ODIM=366 (3x122) channels. It is created by concatenating the potential temperature \\(\theta\\) (122), zonal flux of vertical momentum \\(u'\omega'\\) (122) and the meridional flux of vertical momentum \\(v'\omega'\\) (122) along the vertical dimension. ODIM 0 to 121 correspond to the potential temperature, and so on. 
+
+<h1>File Attributes</h1>
+The netCDF attributes describe the scaling recipe for each variable. To view, execute: ncdump -h (filename)
+<br /><br />
+<h1>Contact</h1>
+<a href="https://github.com/amangupta2" target="_blank">https://github.com/amangupta2</a> or <a href=""mailto:webmaster@example.com">amangupta2@gmail.com</a>