Added more stuff.

_toc.yml

@@ -3,10 +3,24 @@ root: notes/index.md
 chapters:
   - title: Introduction
     sections:
+      - file: notes/project.md
       - file: notes/litreview.md
   - title: Theory
     sections:
       - file: notes/theory/evt
+      - file: notes/theory/eval
+      - file: notes/theory/bayes
   - title: Data
     sections:
-      - file: notes/data/datasets
+      - file: notes/data/datasets
+      - file: notes/data/data_access
+  - title: Modeling
+    sections:
+      - file: notes/modeling/features_manual
+      - file: notes/modeling/features_ai
+      - file: notes/modeling/software
+  - title: Cookbook
+    sections:
+      - file: notes/cookbook/filtering
+      - file: notes/cookbook/anomalies
+      - file: notes/cookbook/spatial_mean

myst.yml

@@ -1,7 +1,8 @@
 # See docs at: https://mystmd.org/guide/frontmatter
 version: 1
 project:
-  title: Bayesian Extreme Value Modeling For Climate
+  title: Bayesian Methods for Extreme Value Modeling
+  subtitle: Applications in Climate
   # description:
   keywords: []
   authors: []

notes/cookbook/anomalies.md

@@ -0,0 +1,124 @@
+---
+title: Anomalies in EO
+subject: Anomalies with Spatiotemporal Data
+short_title: EO Data Anomalies
+authors:
+  - name: J. Emmanuel Johnson
+    affiliations:
+      - CSIC
+      - UCM
+      - IGEO
+    orcid: 0000-0002-6739-0053
+    email: juanjohn@ucm.es
+license: CC-BY-4.0
+keywords: simulations
+abbreviations:
+    ERA5: ECMWF Reanalysis Version 5
+    CMIP6: Coupled Model Intercomparison Project Phase 6
+    AMIP6: Atmospherical Model Intercomparison Project Phase 6
+    PDEs: Partial Differential Equations
+    RHS: Right Hand Side
+    TLDR: Too Long Did Not Read
+    SSP: Shared Socioeconomic Pathways
+    GPD: Generalized Pareto Distribution
+    GEV: Generalized Extreme Value
+---
+
+
+## Climatology
+
+$$
+\begin{aligned}
+\text{Climatology Equation}: && && \bar{y}_c(t) &= \frac{1}{N_s}\sum_{n=1}^{Ns}\boldsymbol{y}(\mathbf{x}_n,t) \\
+\text{Climatology Function}: && && \bar{y}_c&: \Omega_\text{Globe}\times\mathcal{T}_\text{Reference} \rightarrow \mathbb{R}^{D_y} \\
+\text{Spatial Domain}: && && \mathbf{x}&\in\Omega_\text{Globe}\subseteq\mathbb{R}^{D_s}\\
+\text{Temporal Domain}: && && t&\in\mathcal{T}_\text{Reference}\subseteq\mathbb{R}^+
+\end{aligned}
+$$
+
+:::{seealso} Tutorials
+:class: dropdown
+
+[**ClimateMatch**](https://comptools.climatematch.io/tutorials/W1D1_ClimateSystemOverview/student/W1D1_Tutorial5.html).
+An simple tutorial showcasing how the `groupby` function works wrt monthly/seasonal means.
+
+[**Xarray**](https://docs.xarray.dev/en/stable/examples/monthly-means.html).
+A tutorial that showcases how to calculate seasonal averages from time series of monthly means.
+
+:::
+
+## Anomalies
+
+
+There is an error in this formulation because you cannot subtract the climatology from the global time series because they are on different temporal domains.
+
+$$
+\begin{aligned}
+\text{Climatology}: && && 
+\boldsymbol{\bar{y}} &=  \boldsymbol{\bar{y}}_c(t) && && t\in\mathcal{T}_\text{Reference}\subseteq\mathbb{R}^+ \\
+\text{Data}: && &&
+\boldsymbol{y} &= \boldsymbol{y}(\mathbf{x},t)
+&& && t\in\mathcal{T}_\text{Globe}\subseteq\mathbb{R}^+ && && 
+\mathbf{x}\in\Omega\subseteq\mathbb{R}^{D_s}
+\end{aligned}
+$$
+
+From a code perspective, this can be stated where the global data is
+
+```python
+# global data
+data_globe: Array["Nx Ny Nt"] = ...
+# climatology reference period
+data_climatology: Array["Nc"] = ...
+# IMPOSSIBLE to subtract one timeseries from another (even with broadcasting)
+data_anomaly: Array["Nx Ny Nt"] = data_globe - data_climatology
+
+```
+
+**TODO**: Need to figure out how this works.
+
+
+**PsuedoCode**
+
+https://xcdat.readthedocs.io/en/latest/examples/climatology-and-departures.html
+
+### Example 1: Monthly Mean
+
+This example was taken from the [xarray documentation](https://docs.xarray.dev/en/latest/examples/weather-data.html#Calculate-monthly-anomalies).
+
+```python
+# calculate monthly mean
+climatology: xr.Dataset = ds.groupby("time.month").mean("time")
+
+# calculate anomalies
+anomalies: xr.Dataset = ds.groupby("time.month") - climatology
+```
+
+***
+
+### Example 2: Monthly Standardization
+
+We can also calculate the standardized monthly means.
+This implies calculating the monthly mean and standard deviation.
+
+
+```python
+# calculate monthly mean
+climatology_mean: xr.Dataset = ds.groupby("time.month").mean("time")
+climatology_std: xr.Dataset = ds.groupby("time.month").std("time")
+
+# create standardization function
+std_fn = lambda x, mean, std: (x - mean) / std
+
+# calculate anomalies
+anomalies: xr.Dataset = xr.apply_ufunc(
+    std_fn,
+    ds.groupby("time.month"),
+    climatology_mean,
+    climatology_std
+)
+```
+
+***
+
+### Example 3: Seasonal

notes/cookbook/filtering.md

@@ -0,0 +1,105 @@
+---
+title: Filtering EO Data
+subject: Filtering Spatiotemporal Data
+short_title: Filtering EO Data
+authors:
+  - name: J. Emmanuel Johnson
+    affiliations:
+      - CSIC
+      - UCM
+      - IGEO
+    orcid: 0000-0002-6739-0053
+    email: juanjohn@ucm.es
+license: CC-BY-4.0
+keywords: simulations
+abbreviations:
+    ERA5: ECMWF Reanalysis Version 5
+    CMIP6: Coupled Model Intercomparison Project Phase 6
+    AMIP6: Atmospherical Model Intercomparison Project Phase 6
+    PDEs: Partial Differential Equations
+    RHS: Right Hand Side
+    TLDR: Too Long Did Not Read
+    SSP: Shared Socioeconomic Pathways
+    GPD: Generalized Pareto Distribution
+    GEV: Generalized Extreme Value
+---
+
+> This is my quick start guide to filtering Earth Observation data.
+> Filtering is a very useful tool.
+> It can be used for smoothing which can remove high-frequency or low frequency signals.
+> It can also be used to calculate min-max-mean values of a window of data.
+> The unique thing about EO data is that we have spatiotemporal data.
+> So this implies that we will have to often decide whether we want to apply the filter operation along the spatial axis and/or the temporal axis.
+
+## Formulation
+
+Most filtering operations are special cases of convolutions.
+
+$$
+\begin{aligned}
+\text{Convolution Operator}: && && \boldsymbol{\bar{y}}{(\mathbf{x})} &= (\boldsymbol{f} \circledast \boldsymbol{y})(\mathbf{x}) \\
+\text{Continuous Convolution}: && && &= \int_{-\infty}^\infty 
+\boldsymbol{y}(\tau)\boldsymbol{f}(\mathbf{x}-\tau)d\tau \\
+\text{Discrete Convolution}: && && &= \sum_{m=-\infty}^\infty 
+\boldsymbol{y}(m)\boldsymbol{f}(n-m)
+\end{aligned}
+$$
+
+
+Essentially, this is:
+
+1. an element-wise multiplication of data points with filter coefficients.
+2. Performing a mathematical operation on the weighted points within a window.
+
+This is equivalent to the dot product of two vectors, where one vector is the data points within a window and the other vector is the filter coefficients.
+
+***
+
+## From Scratch
+
+
+We can write some basic pseudo-code for filtering.
+We can use some basic filtering
+
+```python
+# define kernel operator
+kernel_size = (5,)
+stride = (1,)
+@kex.kmap(kernel_size=kernel_size, stride=stride)
+def filter_all(u: Float[Array, "... Nt"]):
+    return jnp.average(u)
+```
+
+
+We can use some more advanced filtering methods.
+
+***
+
+## `xarray`
+
+We can use `xarray` to compute the rolling mean
+
+See [docs](https://docs.xarray.dev/en/stable/generated/xarray.DataArray.rolling.html) for more detailed examples.
+
+```python
+# initialize data
+data: Float[Array, "Nt"] = np.linspace(0, 11, num=12)
+coords: pd.DateRange = pd.date_range("1999-12-15", periods=12, freq=pd.DateOffset(months=1))
+
+# create an xarray dataarray
+da: xr.DataArray = xr.DataArray(data, coords, dims="time")
+
+# compute rolling mean over 5 day window
+time_window: int = 5 # 5 Days
+da: xr.DataArray = da.rolling(time=5, center=True).mean()
+
+# (Optional) Remove NANS from end-points
+da: xr.DataArray = da.dropna("time")
+```
+
+***
+
+## `gcm_filter`
+
+There is another package called [gcm-filters](https://gcm-filters.readthedocs.io/en/latest/index.html) which is a convenient wrap-around the `xarray.Dataset`.
+They feature many more advanced filters which take into account things like masks and curvilinear grids.

notes/cookbook/spatial_mean.md

@@ -0,0 +1,45 @@
+---
+title: Spatial Averaging
+subject: Averaging Spatial Data
+short_title: Spatial Averaging
+authors:
+  - name: J. Emmanuel Johnson
+    affiliations:
+      - CSIC
+      - UCM
+      - IGEO
+    orcid: 0000-0002-6739-0053
+    email: juanjohn@ucm.es
+license: CC-BY-4.0
+keywords: simulations
+abbreviations:
+    ERA5: ECMWF Reanalysis Version 5
+    CMIP6: Coupled Model Intercomparison Project Phase 6
+    AMIP6: Atmospherical Model Intercomparison Project Phase 6
+    PDEs: Partial Differential Equations
+    RHS: Right Hand Side
+    TLDR: Too Long Did Not Read
+    SSP: Shared Socioeconomic Pathways
+    GPD: Generalized Pareto Distribution
+    GEV: Generalized Extreme Value
+---
+
+
+This example was taken from the [xarray documentation](https://docs.xarray.dev/en/latest/examples/area_weighted_temperature.html).
+
+
+```python
+weights: xr.Coordinates = np.cos(np.deg2rad(da.lat))
+weights.name = "weights"
+```
+
+:::{seealso} Tutorials
+:class: dropdown
+
+[**xarray**](https://docs.xarray.dev/en/latest/examples/area_weighted_temperature.html).
+An example from `xarray` that showcases the area weighted temperature.
+
+[**xcdata**](https://xcdat.readthedocs.io/en/latest/examples/spatial-average.html).
+An example for calculating geospatial weighted averages from monthly time series.
+:::
+