Update README.md

README.md

@@ -41,20 +41,20 @@ More detailed information about the new parameters introduced with AIFS Single v
 
 | Short Name | Name | Units | Component Type | Lev.Type |
 |:----------:|:----:|:-----:|:--------------:|:--------:|
-| swl1 | Volumetric soil water layer 1 | $m^3 m^{-3}$ | HRES | sfc |
-| swl2 | Volumetric soil water layer 2 | $m^3 m^{-3}$ | HRES | sfc |
-| stl1 | Soil temperature level 1 | $K$ | HRES | sfc |
-| stl2 | Soil temperature level 2 | $K$ | HRES | sfc |
-| 100u | 100 metre U wind component | $m s^{-1}$ | HRES | sfc |
-| 100v | 100 metre V wind component | $m s^{-1}$ | HRES | sfc |
-| ssrd | Surface short-wave (solar) radiation downwards | $J m^{-2}$ | HRES | sfc |
-| strd | Surface long-wave (thermal) radiation downwards | $J m^{-2}$ | HRES | sfc |
-| tcc  | Total cloud cover | $(0 - 1)$ | HRES | sfc |
-| hcc  | High Cloud Cover  | $(0 - 1)$ | HRES | sfc |
-| mcc  | Medium Cloud Cover | $(0 - 1)$ | HRES | sfc |
-| lc   | Low cloud cover | $(0 - 1)$ | HRES | sfc |
-| ro   | Runoff | $m$ | HRES | sfc |
-| sf   | Snowfall | $m$ of water equivalent | HRES | sfc |
+| swl1 | Volumetric soil water layer 1 | \\(m^3 m^{-3}\\) | HRES | sfc |
+| swl2 | Volumetric soil water layer 2 | \\(m^3 m^{-3}\\) | HRES | sfc |
+| stl1 | Soil temperature level 1 | \\(K\\) | HRES | sfc |
+| stl2 | Soil temperature level 2 | \\(K\\) | HRES | sfc |
+| 100u | 100 metre U wind component | \\(m s^{-1}\\) | HRES | sfc |
+| 100v | 100 metre V wind component | \\(m s^{-1}\\) | HRES | sfc |
+| ssrd | Surface short-wave (solar) radiation downwards | \\(J m^{-2}\\) | HRES | sfc |
+| strd | Surface long-wave (thermal) radiation downwards | \\(J m^{-2}\\) | HRES | sfc |
+| tcc  | Total cloud cover | \\((0 - 1)\\) | HRES | sfc |
+| hcc  | High Cloud Cover  | \\((0 - 1)\\) | HRES | sfc |
+| mcc  | Medium Cloud Cover | \\((0 - 1)\\) | HRES | sfc |
+| lc   | Low cloud cover | \\((0 - 1)\\) | HRES | sfc |
+| ro   | Runoff | \\(m\\) | HRES | sfc |
+| sf   | Snowfall | \\(m\\) of water equivalent | HRES | sfc |
 
 
 #### Changes to existing parameters 
@@ -171,22 +171,22 @@ to the fact that for AIFS Single v0.2.1 we used just operational-analysis data f
 release we have done the fine-tunning from 2016 to 2022. 
 
 The other important change in the fine-tuning stage is that for AIFS Single v0.2.1 after the 6hr model training the
-optimiser was not restarted (ie. rollout was done with the minimal lr of $3 × 10^{-7}$). For this release we have seen
+optimiser was not restarted (ie. rollout was done with the minimal lr of \\(3 × 10^{-7}\\)). For this release we have seen
 that restarting the optimiser for the rollout improves the model's performance. For the operational-fine tuning rollout
 stage, the learning rate cycle is restarted, gradually decreasing to the minimum value at the end of rollout.
 
 <!-- This relates heavily to the Technical Specifications. Content here should link to that section when it is relevant to the training procedure. -->
 
 - **Pre-training**: It was performed on ERA5 for the years 1979 to 2022 with a cosine learning rate (LR) schedule and a
-total of 260,000 steps. The LR is increased from 0 to $10^{-4}$ during the first 1000 steps, then it is annealed to a
-minimum of $3 × 10^{-7}$. The local learning rate used for this stage is $3.125 × 10^{-5}$.
+total of 260,000 steps. The LR is increased from 0 to \\(10^{-4}\\) during the first 1000 steps, then it is annealed to a
+minimum of \\(3 × 10^{-7}\\). The local learning rate used for this stage is \\(3.125 × 10^{-5}\\).
 - **Fine-tuning**: The pre-training is then followed by rollout on operational real-time IFS NWP analyses for the years
-2016 to 2022, this time with a local learning rate of $8 × 10^{−7}$, which is decreased to $3 × 10^{−7}$. Rollout steps
+2016 to 2022, this time with a local learning rate of \\(8 × 10^{−7}\\), which is decreased to \\(3 × 10^{−7}\\). Rollout steps
 increase per epoch. In this second stage the warm up period of the optimiser is 100 steps to account for shorter length
 of this stage. Optimizer step are equal to 7900 ( 12 epoch with ~630 steps per epoch).
 
 As in the previous version of aifs-single for fine-tuning and initialisation of the model during inference, IFS fields
-are interpolated from their native O1280 resolution (approximately $0.1°$) down to N320 (approximately $0.25°$). 
+are interpolated from their native O1280 resolution (approximately \\(0.1°\\)) down to N320 (approximately \\(0.25°\\)). 
 
 #### Training Hyperparameters