The following describes each formula included in the Grids Formulas section of McIDAS-V.

• Time Steps
• Ensemble

• Define a grid diagnostic (gddiag) - Defines a grid diagnostic to perform.

• Input Parameter	Definition
  gddiag	Grid diagnostic. For more information, see the Grid Diagnostics section of Jython Library.

• Find latitude of grid points (fieldimpl) - Obtains the latitude coordinate from the grid at each location and plots the latitude at each point on the map.
• Find longitude of grid points (fieldimpl) - Obtains the longitude coordinate from the grid at each location and plots the longitude at each point on the map.
• Horizontal Advection (from %N1% & %N2%) (scalar parameter, U Component, V Component) - Calculates horizontal advection from U and V components.

• Input Parameter	Definition
  scalar parameter	Scalar Parameter (the parameter that will be mapped).
  U Component	The u-component of the wind.
  V Component	The v-component of the wind.

• Horizontal Flux Divergence (from %N1% & %N2%) (scalar parameter, U Component, V Component) - Calculates horizontal flux divergence from u and v components.

• Input Parameter	Definition
  scalar parameter	Scalar Parameter (the parameter that will be mapped).
  U Component	The u-component of the wind
  V Component	The v-component of the wind.

• Layer Difference (Top of Layer, Bottom of Layer) - Calculates a layer difference between a field at two different levels. Note that you must select a 3D field to use this formula.

• Input Parameter	Definition
  Top of Layer	Top layer (default=500)
  Bottom of Layer	Bottom layer (default=1000)

• Layer Wind Shear (top, bottom) - Calculates the wind shear between two user-defined layers. Note that you must select 3D fields to use this formula.

• Input Parameter	Definition
  top	Top layer (default=500)
  bottom	Bottom layer (default=850)

• Make flow vectors from grid relative u and v data (u, v) - Calculates true wind vectors based off of relative u and v data after user inputs the field and desired levels. You can utilize 2D or 3D fields.

• Input Parameter	Definition
  u	The u-component of the wind.
  v	The v-component of the wind.

• Make flow vectors from u and v data (u, v) - Creates flow vectors based off of the 2D u and v parameters entered by the user.

• Input Parameter	Definition
  u	The u-component of the wind.
  v	The v-component of the wind.

• Make flow vectors from u, v, and w data (u, v, w) - Creates flow vectors based off of the 3D u and v parameters entered by the user. These flow vectors are then scaled based off the user-entered w parameter.

• Input Parameter	Definition
  u	The u-component of the wind.
  v	The v-component of the wind.
  w	The w-component of the wind (vertical velocity).

• Make slice 2D (slice) - Creates a 2D slice from a 3D display at a single level.

• Input Parameter	Definition
  slice	The parameter utilized to create the display.

• One value colored by another (Data field, Color field) - Creates an image of the data chosen in the Data field, and colors the data with the color scheme of the Color field parameter.

• Input Parameter	Definition
  Data field	The parameter that is mapped in the display.
  Color field	The parameter whose color field will be used to plot the parameter selected under Data field.

• Resample grid (grid, gridwithNewDomain) - Displays gridded data on a new domain.

• Input Parameter	Definition
  grid	The parameter that is mapped in the display.
  gridwithNewDomain	The parameter whose domain will be used to plot the parameter selected under grid.

• Simple time difference in one parameter (Time 1, Time 2) - Creates an image representing the numerical difference in the value of the chosen parameter between the two time steps selected by the user. Time 1 is the initial time step and Time 2 is the second time step. For example, if you select Time 1 to be 10, and Time 2 to be 0, then the formula will utilize the most recent time, and the 10th most recent time. The difference in the parameter is done by Time 2 - Time 1.

• Input Parameter	Definition
  Time 1	First time (default=1)
  Time 2	Second time (default=0)

• Slice at Altitude (Altitude, Unit) - Extracts a 2D horizontal slice from a 3D grid at the given altitude and maps an image.

• Input Parameter	Definition
  altitude	Altitude to slice.
  unit	Specify a unit. It must be compatible with meters (ft, fathoms, etc.)

• Slice at Level (Level) - Extracts a 2D horizontal slice from a 3D grid at a level and maps the image.

• Input Parameter	Definition
  level	Level to slice. Must be appropriate for the grid.

• Speed from 2 components (x, y) - Calculates speed from the user-chosen x and y components and displays an image.

• Input Parameter	Definition
  x	The x-component of the wind.
  y	The y-component of the wind.

• Wind Shear Vectors (top, bottom) - Calculates the u and v layer difference and returns a map of vectors.

• Input Parameter	Definition
  top	Top layer (default=500)
  bottom	Bottom layer (default=850)

• Accumulate from initial timestep - Plots the specified parameter in the Main Display window. Each frame is a total of the parameter at the time in addition to the total value of the parameter in previous time steps. The formula to compute this is as follows, where T represents the current time step, and numbers 0, 1, etc. represent the previous time steps:

• D(T) = D(0) + D(1) + .. + D(T)

• Average Time steps - Plots one map representing the average value of the specified parameter at any one point on the map during the time sequence selected.
• Difference from initial timestep - Plots a sequence of images. Each image maps the difference in the numerical value of the parameter from the initial values of the first frame. This formula sets the value of each time step N as:

• D(T) = D(T) - D(0)

• Max over time steps - Plots one map representing the highest value of the specified parameter at any point on the map during the time sequence selected.
• Merge time sequences - Creates a loop of images where while the images will be in order with respect to time, you do not need to load in every time step.
• Min over time steps - Plots one map representing the lowest value of the specified parameter at any one point on the map during the time sequence selected.
• Running Average (No. of Steps, End Point Option) - Generates a running average of your specified parameter and plots the data in the Main Display window.

• Input Parameter	Definition
  No. of steps	The number of steps to average over.
  End Point Option	The option for unsmoothed end points. 0 = set to missing; 1 = use symmetry; -1= assume cyclic

• Time step difference - Plots a sequence of images. Each frame plots the value of the specified parameter at that time, and subtracts from it the value of the same parameter at the previous time in the loop.

• D(T) = D(T) - D(T-1)

• Time step sum - Plots a sequence of images. Each frame plots the value of the specified parameter at that time, and adds to it the value of the same parameter at the previous time step in the loop.

• D(T) = D(T) + D(T-1)

• Total sum over times - Plots one image with the total value of your selected parameter summed up over your chosen number of time steps.
• Weighted running average (Weights, End Point Option) - Generates an image of the weighted running average of your selected parameter.

• Input Parameter	Definition
  Weights	The weight you wish to give to your running average. Separate multiple values with a comma.
  End Point Option	The option for unsmoothed end points. 0 = set to missing; 1 = use symmetry; -1= assume cyclic

• Ensemble average over all grid members - Averages the chosen ensemble members over each time step and plots the data.
• Ensemble grid highest values - Takes the highest numerical value of the chosen parameter over the chosen number of ensemble members and plots the data.
• Ensemble grid lowest values - Takes the lowest numerical value of the chosen parameter over the chosen number of ensemble members and plots the data.
• Ensemble grid mode values - Takes the mode value of the chosen parameter over the chosen number of ensemble members and plots the data.
• Ensemble grid percentile values - Plots the ensemble average at the chosen percentage. The higher the percentage, the higher the values plotted in the display will be.
• Ensemble grid range of values - Takes the difference between the upper bound and lower bound of the chosen parameter over the chosen number of grid ensembles and plots the result.
• Ensemble grid standard deviation - Plots the standard deviation of the chosen parameter over the chosen number of ensemble members.
• Ensemble grid univariate probability - Plots the probability that certain user-provided conditions will be met for the specified parameter.

• Input Parameter	Definition
  P(GridVaiable lt|gt a)	The mathematical operation (less than or greater than) that will operate around value 'a'.
  a	The value used by the operator chosen above.
  P1 (and|or) P2	Determines if you want to display the probability of threshold values 'a' or 'b' to both be used to create the display, or if you want one or the other to work.
  P(GridVariable lt|gt b) (optional)	The mathematical operation (less than or greater than) that will operate around value 'b'.
  b (optional)	The value used by the operator chosen above.
  Expected Lower Bound (optional)	The expected lower numerical bound of your chosen field.
  Expected Upper Bound (optional)	The expected upper numerical bound of your chosen field.

• Example: P=gt, a=90000, P1=and, P=lt, b=100000, field='Pressure reduced to MSL'. In this example, probabilities will be mapped in the Main Display window for the chosen number of times/ensemble members that the pressure will be greater than 90,000 Pa and that the pressure is less than 100,000 Pa.