documentation: spell checking

docs/src/how_to_run_speedy.md

@@ -1,6 +1,9 @@
 # How to run SpeedyWeather.jl
 
-Creating a SpeedyWeather.jl simulation and running it consists conceptually of 4 steps
+Creating a SpeedyWeather.jl simulation and running it consists conceptually of 4 steps.
+In contrast to many other models, these steps are bottom-up rather then top-down.
+There is no monolithic interface to SpeedyWeather.jl, instead all options that a
+user may want to adjust are chosen and live in their respective model components.
 
 1. Create a [SpectralGrid](@ref) which defines the grid and spectral resolution.
 2. [Create model components](@ref create_model_components) and combine to a [model](@ref create_model).

docs/src/shallowwater.md

@@ -106,7 +106,7 @@ In spectral space ``\nabla^2`` is a diagonal operator, meaning that there is no
 harmonics and its inversion is therefore easily done on a mode-by-mode basis of the harmonics.
 
 This can be made use of when facing time stepping constraints with explicit schemes, where
-ridiculuously small time steps to resolve fast waves would otherwise result in a horribly slow simulation. 
+ridiculously small time steps to resolve fast waves would otherwise result in a horribly slow simulation. 
 In the shallow water system there are gravity waves that propagate at a wave speed of ``\sqrt{gH}``
 (typically 300m/s), which, in order to not violate the
 [CFL criterion](https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition)
@@ -219,7 +219,7 @@ The idea of the semi-implicit time stepping is now as follows:
 Some notes on the semi-implicit time stepping
 
 - The inversion of the semi-implicit time stepping depends on ``\delta t``, that means every time the time step changes, the inversion has to be recalculated.
-- You may choose ``\alpha = 1/2`` to dampen gravity waves but initialisation shocks still usually kick off many gravity waves that propagate around the sphere for many days.
+- You may choose ``\alpha = 1/2`` to dampen gravity waves but initialization shocks still usually kick off many gravity waves that propagate around the sphere for many days.
 - With increasing ``\alpha > 1/2`` these waves are also slowed down, such that for ``\alpha = 1`` they quickly disappear in several hours.
 - Using the [scaled shallow water equations](@ref scaled_swm) the time step ``\delta t`` has to be the scaled time step ``\tilde{\Delta t} = \delta t/R`` which is divided by the radius ``R``. Then we use the normalized eigenvalues ``-l(l+1)`` which also omit the ``1/R^2`` scaling, see [scaled shallow water equations](@ref scaled_swm) for more details.
 

docs/src/spectral_transform.md

@@ -354,7 +354,7 @@ number ``m`` times imaginary ``i``.
 ### Meridional derivative
 
 The meridional derivative of the spherical harmonics is a derivative of the Legendre polynomials for which the following
-recursion relation applies[^Randall2021],[^Durran2010],[^GFDL]
+recursion relation applies[^Randall2021],[^Durran2010],[^GFDL],[^Orszag70]
 
 ```math
 \cos\theta \frac{dP_{l,m}}{d\theta} = -l\epsilon_{l+1,m}P_{l+1,m} + (l+1)\epsilon_{l,m}P_{l-1,m}.
@@ -394,7 +394,7 @@ degree ``l``, but scalar quantities should not make use of it. Equivalently, the
 set to zero before the time integration, which only advances scalar quantities.
 
 
-In SpeedyWeather.jl vector quantities
+In SpeedyWeather.jl, vector quantities
 like ``u,v`` use therefore one more meridional mode than scalar quantities such as vorticity ``\zeta`` or stream
 function ``\Psi``. The meridional derivative in SpeedyWeather.jl also omits the ``1/R``-scaling as explained for
 the [Zonal derivative](@ref) and in [Radius scaling](@ref scaling).
@@ -443,7 +443,7 @@ The spectral Laplacian is easily applied to the coefficients ``\Psi_{lm}`` of a
 as the spherical harmonics are eigenfunctions of the Laplace operator ``\nabla^2`` in spherical
 coordinates with eigenvalues ``-l(l+1)`` divided by the radius squared ``R^2``, i.e.
 ``\nabla^2 \Psi`` becomes ``\tfrac{-l(l+1)}{R^2}\Psi_{lm}`` in spectral space. For example,
-vorticity ``\zeta`` and streamfunction ``\Psi`` are related by ``\zeta = \nabla^2\Psi``
+vorticity ``\zeta`` and stream function ``\Psi`` are related by ``\zeta = \nabla^2\Psi``
 in the barotropic vorticity model. Hence, in spectral space this is equivalent for every
 spectral mode of degree ``l`` and order ``m`` to
 
@@ -502,3 +502,4 @@ as further described in [Radius scaling](@ref scaling).
 [^GFDL]: Geophysical Fluid Dynamics Laboratory, [The barotropic vorticity equation](https://www.gfdl.noaa.gov/wp-content/uploads/files/user_files/pjp/barotropic.pdf).
 [^FFT]: Depending on the implementation of the Fast Fourier Transform ([Cooley-Tukey algorithm](https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm), or or the [Bluestein algorithm](https://en.wikipedia.org/wiki/Chirp_Z-transform#Bluestein.27s_algorithm)) *easily Fourier-transformable* can mean different things: Vectors of the length ``n`` that is a power of two, i.e. ``n = 2^i`` is certainly easily Fourier-transformable, but for most FFT implementations so are ``n = 2^i3^j5^k`` with ``i,j,k`` some positive integers. In fact, [FFTW](http://fftw.org/) uses ``O(n \log n)`` algorithms even for prime sizes.
 [^Bourke72]: Bourke, W. An Efficient, One-Level, Primitive-Equation Spectral Model. Mon. Wea. Rev. 100, 683–689 (1972). doi:[10.1175/1520-0493(1972)100<0683:AEOPSM>2.3.CO;2](https://doi.org/10.1175/1520-0493(1972)100<0683:AEOPSM>2.3.CO;2)
+[^Orszag70]: Orszag, S. A., 1970: Transform Method for the Calculation of Vector-Coupled Sums: Application to the Spectral Form of the Vorticity Equation. J. Atmos. Sci., 27, 890–895, [10.1175/1520-0469(1970)027<0890:TMFTCO>2.0.CO;2](https://doi.org/10.1175/1520-0469(1970)027<0890:TMFTCO>2.0.CO;2). 

docs/src/speedytransforms.md

@@ -38,7 +38,7 @@ map = gridded(alms)
 ```
 By default, the `gridded` transforms onto a [`FullGaussianGrid`](@ref FullGaussianGrid) unravelled here
 into a vector west to east, starting at the prime meridian, then north to south, see [RingGrids](@ref).
-We can visualize `map` quickly with a unicodeplot via `plot` (see [Visualising RingGrid data](@ref))
+We can visualize `map` quickly with a UnicodePlot via `plot` (see [Visualising RingGrid data](@ref))
 ```@example speedytransforms
 plot(map)
 ```
@@ -108,7 +108,7 @@ Note that because we chose `dealiasing=3` (cubic truncation) we now match a T5 s
 with a 12-ring octahedral Gaussian grid, instead of the 8 rings as above. So going from
 `dealiasing=2` (default) to `dealiasing=3` increased our resolution on the grid while the
 spectral resolution remains the same. The `SpectralTransform` also has options for the
-recomputation or precomputation of the Legendre polynomials, fore more information see
+recomputation or pre-computation of the Legendre polynomials, fore more information see
 [(P)recompute Legendre polynomials](@ref).
 
 Passing on `S` the `SpectralTransform` now allows us to transform directly on the grid
@@ -164,7 +164,7 @@ m = Matrix(map) # hide
 m
 ```
 You hopefully know which grid this data comes on, let us assume it is a regular
-latitde-longitude grid, which we call the `FullClenshawGrid`. Note that for the spectral
+latitude-longitude grid, which we call the `FullClenshawGrid`. Note that for the spectral
 transform this should not include the poles, so the 96x47 matrix size here corresponds
 to