Time

Time is a very important dimension in meteorology, and there are many things to keep in mind. Here we will explore how Metview handles the fourth dimension.

Overlaying Time Steps

Inspect the supplied GRIB files: z500_fc.grib contains geopotential forecasts made in one run, but for six different forecast steps; z500_an.grib contains analysis fields for two times. Visualise the supplied Geographical View icon and drop the forecast GRIB icon along with its corresponding Contouring icon (cont_fc)into the Display Window, and then drop the analysis GRIB icon along with its corresponding Contouring icon (cont_an)too. Go through the frames of animation. The fields have been overlaid, but if you look at the times and dates in the title, you will see that they do not match. Metview has simply plotted the first field of each data file together, then the second, and so on. We can make it more intelligent.

Edit the Geographical View icon and set this:

Save the icon, visualise it and drop the data with their visdefs in again. Go through the animation steps and look at the Frames tab in the Display Window to see what has happened. Now the fields will be overlaid only if their valid date and time match.

Metview's overlay rules

To summarise, Metview's overlay rules can be described like this:

In practice, this means that a GRIB file with 5 fields is visualised as 5 separate plots which you can scroll through.

If you wish to overlay data, then you must provide separate data icons for each 'layer'. Then we are subject to Rule 2:

Precipitation

Precipitation data provides an interesting challenge. Precipitation fields in MARS are stored as accumulated fields. Visualise the supplied precip.grib icon with the precip_shade visdef. The first field is empty (check using the Cursor Data). The first field has a step of 0, meaning that it contains the total precipitation accumulated between the run time and the run time plus step. Since these are the same, there is no accumulated precipitation! Subsequent steps show more and more precipitation (the amount accumulated over 3, 6, 9, etc hours).

What if we want to plot just the rain that accumulated between 06:00 and 09:00? That would be the accumulated precip at 09:00 minus the accumulated precip at 06:00. We can compute this in a macro.

Create a new Macro icon and rename it compute_precip.

We can see from examining the file that the 6 and 9 o-clock steps are fields 3 and 4 respectively (using 1-based indexing). So the following macro code will compute the difference and return it:

precip = read("precip.grib")

precip_6_to_9 = precip[4] - precip[3]
return precip_6_to_9

Visualise the macro to plot it.

Now we want to go further and compute the precipitation for each and every 3-hour period. We can do this with more complex field indexing.

So we want field 2 minus field 1, field 3 minus field 2, etc. We can do this in a single line of code because we can handle multiple fields in a single operation as shown:

To extract fields 1 to 4, for example, we can use the following syntax:

fields = precip[1,4]

So the following piece of code will do what we want in a more general way:

precip = read("precip.grib")

n = count(precip) # the number of fields in the fieldset
precip_3h = precip[2, n] - precip[1, n-1]
return precip_3h

Visualise the macro. Your plot may be blank! There is one more trick: we have created a derived field, and this changes the automatic scaling algorithm used when plotting. Precipitation is stored in metres, but we want to display it in mm. Modify the precip_shade icon and set:

Visualise your macro result again and confirm that you now have precipitation only for the 3-hour periods, which does not accumulate with each frame.

Note that the meta-data for each field is taken from the first field in each subtraction; "step9 minus step6" returns a field with meta-data from step9, so be aware of this. Macro has functions for setting GRIB meta-data if you need to change it in order to correctly describe the new data.

Dates in Macro

Macro has specific date-handling abilities. Dates are a built-in data type which in fact describe both a date and a time.

Defining dates

You can create date variables in a number of ways:

• yyyy-mm-dd
• yyyy-DDD  (DDD is a 3-digit Julian day, e.g. 365 is 31st December in non-leap years)

These will have the time set to 00:00. A different time can be added by adding

• HH:MM
• HH:MM:SS

Create a new Macro icon, rename it to dates and define a date:

d1 = 2015-03-11
print(type(d1))
print(d1)

Try adding a time:

d1 = 2015-03-11 12:00

Converting numbers into dates

The date() function converts numbers into dates using the same syntax that MARS understands. For example:

• d1 = date(20150105)
• today = date(0)
• yesterday = date(-1)

This syntax can be useful if reading dates from a text file or some other source.

Again, the time will be 00:00 unless we add it. We can consider the time to be a fraction of a day:

• midday = date(20150105.5)

Use this syntax to add another variable, d2, which contains the date and time for 13:00h at 2015-03-13. Print it to check it.

Note that when passing numeric dates such as 20150105 to other modules, such as the MARS Retrieval module, these do not need to be converted into date variables. However, MARS treats Date and Time as separate parameters, so a date variable would need to be split into these components.

Date arithmetic

When dealing with dates, the number 1 represents one day. So the expression d1 + 1 gives a date one day later than day 1. To compute the difference, in days, between two dates, it's simply:

• diff = d2 - d1

Times can be added as fractions of days, and there are some helper functions too:

• d1 = d1 + 0.5                               # add 12 hours
• d1 = d1 + hour(12)                          # hour(12) returns 0.5
• d1 = d1 + hour(23) + minute(58) + second(0) # 2 minutes to midnight

Compute and print the difference between your two dates, d2 and d1.

Looping through dates

Three examples (no need to type these in, but the code is in a macro called dates in the solutions folder), to get a feel for it:

for d = 2015-01-01 to 2015-03-01 do
    print(d)  # each step is 1 day
end for

for d = 2015-01-01 to 2015-03-01 by 2 do
    print(d)  # each step is 2 days
end for

for d = 2015-01-01 to 2015-03-01 by hour(6) do
    print(d)  # each step is 6 hours
end for

Computing the precipitation rate at a point

As an exercise to put all of this together, we will write a new macro to compute the precipitation rate in mm per hour at a  particular location for each time step. The steps will be:

• compute the 'period' precipitation from precip.grib - this is what we already did earlier, so it's done! Just copy the code to your new macro and change the result variable name to precip_diff
• loop through the fields in the original fieldset and for each:
  • get the date and time of the forecast step (see the hint later)
  • combine these into a Metview date variable
  • add it to a list (which was initialised to nil before the loop)
• use syntax similar to the line of code used to compute the 'period' precipitation to find the differences between the times of adjacent fields (ok, we know it's 3 hours, but in theory it could be anything)
• extract the point value for each field in precip_diff (use the nearest_gridpoint() function). Choose a location with some high precipitation
• scale up from metres (as the data are stored) to mm by multiplying by 1000
• convert this into a rate, mm per hour, using the time differences computed earlier

Here are some hints to help.

A list is built up like this:

dates = nil
for i = .... do
    dt = .....  # construct a date/time variable
    dates = dates & [dt]
end for

You can get the date and time of a field as numbers like this, inside the loop, where i is the field index:

d = grib_get_long(precip_diff[i], 'validityDate')
t = grib_get_long(precip_diff[i], 'validityTime')

then combine those numbers into proper date variables. Print the results of these function calls to check exactly what they are returning before you try to convert them into date variables. You will need to divide the time variable (t) to convert it into a fraction of a day before adding it to the date variable (d). The result can be converted with the date() function into a proper date.

Now that you have a list of proper date variables, you can find the difference between consecutive dates using a single line of code which subtracts one set of list elements from another (very similar to computing the 'period precipitation' we did earlier). Now you have a list of time differences in days. You can multiply by 24 to get them in hours.

The nearest_gridpoint() function is now used to get the precipitation values. It can be called in a number of ways, but we will use it like this:

 values = nearest_gridpoint(precip_diffs, lat, lon)

The result is a list of values, a value for each field. You can directly multiply a list variable by a number to obtain a new list where each element has been multiplied - do this to scale from metres to mm.

The final calculation requires converting the data values into mm per hour - divide this list of precipitation values by the list of time differences, which should be in hours (e.g. if the time difference between two steps is 7 hours, then the rate of precip per hour is the mean precip value divided by 7).

Print the result - it will be a list of numbers, one for each time period.

Computing a climatology

The supplied GRIB file era_t2m_jan_2009_2013.grib contains 2 metre temperature fields from the ERA Interim data set, interpolated onto a low-resolution 5x5 degree grid. The data are from years 2009 to 2013 and only include the month of January. The data are also from two times: 00:00 and 12:00. Check that all of this is true!

We will compute a small climatology dataset, which will simply be the mean of all these fields. Write a small macro to do this - it should be just 2 lines long: one to read the GRIB file, and one to compute the mean (simply the mean() function). Return or plot the result to confirm that it looks sensible.

Often, these climatological averages are computed individually for each time step. So in our case, we want to now produce two means: one for all the fields at 00:00 and one for all the fields at 12:00. Hint: use the GRIB Filter icon (and its equivalent Macro code) to extract all the fields where Time = 0 and compute their mean. Do the same with all the 12:00 fields. Concatenate the two mean fields into a 2-field fieldset and plot it.

Extracting dates from other data types

Geopoints

To extract dates from a geopoints file/variable, use the dates() Macro function. Try it on the supplied geopoints file to see what it returns.

BUFR

The easiest way to extract dates from a BUFR file is to convert it to geopoints using the Observation Filter and then extract the dates from the resulting geopoints.

Other formats

Extracting dates from other formats can be more tricky and will not be covered here.

Extra Work

If you have time, try the following.

Computing monthly anomalies

Continuing from the section "Computing a climatology", we will now take some data from 2014 and compute its difference from the climatology data we produced.

Examine the supplied GRIB file era_t2m_jan_2014.grib. It contains low-resolution temperature fields (4x4 degree) from the ERA Interim data set for each day in January 2014 at time steps 00:00 and 12:00. Try the following in a new macro:

1. separate the data into the two different time steps and compute the mean field for each. The end result should be two fields - one is the mean of all the 00:00 fields and the other is the mean of all the 12:00 fields.
2. for each time step, compute the difference between the 2014 mean and the climatological mean computed earlier (you may wish to combine both macros into a single macro at this point)
   1. note that the two data sets are on different grids - you will need to change one of them to the other's grid
3. plot the result (it should be two fields) with Contouring icons appropriate for showing temperature anomalies.

Your result shows the monthly anomalies for January 2014 compared with the previous 5 years.

Finding points with large anomalies

See if you can find the points which have anomalies over a certain threshold (e.g. 4 degrees). Create a geopoints variable with the result.

One possible way to do it:

• convert the anomaly field to geopoints (conversion to geopoints only works with one field at a time)
• use the filter() and abs() functions to find just the absolute values greater than 4
• plot with customised Symbol Plotting icons (we could take the ones used in the Processing Data tutorial)
• these points could be written to a file

In Missing Values and Masks, we will see how we could do this sort of thing directly with the GRIB fields.