Visualising seasonal-diurnal trends in wind observations

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Valentine Bridges
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This attribute is so difficult to reproduce in computers that trends in the statistics of large datasets may remain undetected.

1 Visualising seasonal-diurnal trends in wind observations Nicholas J. Cook Highcliffe on Sea, Dorset Introduction One of the most amazing inherent attributes of the human brain is its ability to see patterns in visual data. This attribute is so difficult to reproduce in computers that trends in the statistics of large datasets may remain undetected. A format for charting wind observations is proposed here that provides an overall view of seasonal and diurnal trends, whether these are obvious as at Singapore or more subtle in form as at Elmdon (West Midlands). Many observers will be familiar with the frequency table, which is a conventional form of reporting wind observations that is compiled by counting the number of observations that lie within given intervals, or bins of speed and direction. One of the first sets of frequency tables for the United Kingdom was published as Met.O.2 (Shellard, 1) for 35 UK anemograph stations over the period 15 15, using the speed intervals of the Beaufort scale and direction increments of, for each (a) calendar month and for the whole year. As these monthly frequency tables were compiled irrespective of the time of day, all diurnal trends were averaged out. Revealing diurnal trends requires binning by hour of day, but revealing their seasonal dependence that is, seasonal-diurnal effects requires binning by month and by hour of day. The procedure is to count the number of observations of each 1kn wind speed and 1 direction that occurs for a given hour of day (in local time) and calendar month. There being h in the day and months, this gives 2 tables in the sequence, from h in January to h in December, which may be designated the monthhour index. The long observation periods of hourly observations now archived make the compilation of these tables a practical proposition, but the large number of tables makes locating seasonal-diurnal trends within them very difficult. The seasonal-diurnal chart A solution to this problem is proposed here. The frequency tables for each hour of the day in a given month may be represented Figure 1. Graphical presentation of diurnal wind speed and direction at Changi, Singapore, for the month of April. (a) Wind speed tile. (b) Wind direction tile. (b) graphically as a contour-surface or tile, as shown in Figure 1. Here, the hour of day in local time is the horizontal axis, the wind speed (Figure 1(a)) or direction (Figure 1(b)) value is the vertical axis and the frequency value represented by a colour. In this format, all the information contained in a conventional wind rose diagram is represented by a single vertical strip through the tile. As wind direction is cyclic, the quadrant from to is repeated as 3 to to show features around north that would otherwise be sliced in two (Figure 1(b)). In all the tiles that follow, a consistent colour scale has been used for the frequency, but the key to these colours has not been provided because this presentation is intended to indicate trends only. These tiles present data from three dimensions: hour of day and observation value as the horizontal and vertical axes, and the frequency count or probability density as the colour, corresponding to a single month. Revealing seasonal trends requires all the calendar months to be added as a fourth dimension. The seasonal-diurnal chart for the whole year is formed by a mosaic of the tiles for each of the calendar months placed side by side: from January on the left to December on the right (as shown later by the legend at the top of each chart in Figures 2 4) and with the wind speed tiles placed immediately above the wind direction tiles. The horizontal axis still records the hour of day (in local time), but this repeats for every calendar month so that for June represents the frequency table for h (local time) in June compiled from all the days of that month in the whole observational record. In this way the trends in the 2 frequency tables become visible in a single chart. The three examples presented below illustrate how well this format reveals seasonaldiurnal trends in wind observations. Changi, Singapore Figure 2 shows this chart for Changi, Singapore. Located within a degree of the Equator, Singapore has two main seasons: the wet monsoon from December to March, and the dry monsoon from June to September with transitions between these two seasons. The surrounding terrain is flat, Weather April 2, Vol. No. 4

Weather April 2, Vol. No. 4 Visualising seasonal-diurnal wind trends Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 2.

The speed chart shows a diurnal cycle between stronger winds around midday and lighter winds before dawn throughout the year, but stronger in the wet monsoon.

lulls, with virtually no contributions from other wind directions.

These are well known attributes of the Singapore wind climate: but the chart also shows that the northerly night-time lulls of the wet monsoon continue through

2 Weather April 2, Vol. No. 4 Visualising seasonal-diurnal wind trends Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 2. Seasonal-diurnal chart for Changi, Singapore. so no orographic effects are expected. The speed chart shows a diurnal cycle between stronger winds around midday and lighter winds before dawn throughout the year, but stronger in the wet monsoon. In the direction chart, the wet monsoon displays two peaks: switching between northeast during the daytime stronger speeds and north during the night-time lulls, with virtually no contributions from other wind directions. The dry monsoon also displays two peaks: southwest during the daytime stronger speeds and southeast during the night-time lulls. These are well known attributes of the Singapore wind climate: but the chart also shows that the northerly night-time lulls of the wet monsoon continue through the wet to dry transition, then back to northwest and persist at a lower frequency through the dry monsoon before veering to northeast again through the dry to wet transition Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 Figure 3. Seasonal-diurnal chart for Jersey (Channel Islands)

4 the direction chart shows a strong diurnal effect, starting in March in the late afternoon, strengthening and occurring earlier in the day during the summer, peaking at h from 2.

3 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 4. Seasonal-diurnal chart for Elmdon (West Midlands) Visualising seasonal-diurnal wind trends Weather April 2, Vol. No. 4 the direction chart shows a strong diurnal effect, starting in March in the late afternoon, strengthening and occurring earlier in the day during the summer, peaking at h from 2. This effect weakens from September onwards and is absent through the winter. There is a secondary component of springtime northeasterly winds in the middle of the night from March through May. Hence the sea land breeze cycle at Jersey is revealed to be mainly a polarisation of wind direction without a significant change in speed. Elmdon (West Midlands) Figure 5. Worksheet Source. Jersey (Channel Islands) The sea land breeze cycle at Jersey was described in an earlier article in Weather (Cook, 2) and the seasonal-diurnal chart in Figure 3 provides a complementary overview. The speed chart shows a gradual seasonal variation between lower speeds in summer and higher speeds in winter, but not much diurnal variation. However, Elmdon is more or less in the geographical centre of England and Wales, so is at the furthest distance from the sea in any direction as is possible in the United Kingdom probably far enough inland to avoid the sea land breeze cycle. It lies on the eastern side of the city of Birmingham in gently undulating countryside. The corresponding seasonal-diurnal chart is shown as Figure 4. As for Jersey, the overall shape of the speed chart dips in the centre showing, as expected, that wind speeds are generally lighter in the summer and stronger in the winter. Superimposed on this is a clear daily cycle of wind speed, strongest in the summer and peaking around h, which is less well organised but still discernible in the winter, peaking at h a cycle that does not occur at Jersey. Unlike Jersey, there is no corresponding diurnal polarisation of wind direction, suggesting that the diurnal

Weather April 2, Vol. No. 4 Visualising seasonal-diurnal wind trends Figure. Worksheet D : compiling the frequency tables. Figure. Worksheet D : compiling the raw probability density.

It is presumably caused by a general increase in convective activity from diurnal heating of the surrounding land, causing breezes from all directions.

4 Weather April 2, Vol. No. 4 Visualising seasonal-diurnal wind trends Figure. Worksheet D : compiling the frequency tables. Figure. Worksheet D : compiling the raw probability density. variation of speed is not organised like the onshore/offshore cycle expected near a coast. It is presumably caused by a general increase in convective activity from diurnal heating of the surrounding land, causing breezes from all directions. The direction chart shows a main horizontal band at, corresponding to the prevailing wind direction for the southern United Kingdom, with some seasonal but little diurnal variation. In the spring, April to May, there is an increase in winds from the northeast, as at Jersey but with less diurnal variation. Creating these charts The charts in this article were created from tables in three worksheets of a Microsoft Excel workbook: Source containing the observational data, V containing the wind speed tables and D containing the wind direction tables. Figure 5 shows the layout of Source : the first three columns contain: (A) the date/time (UTC), (B) the direction and (C) the wind speed for each observation. Column D contains the month index and E contains the hour of day index in local time. Cell E4 is selected in order to display the formula (fx) for the hour of day: = mod(hour(a4)+$e$1,), showing that the local time offset from UTC in cell $E$1 is added to the UTC hour of day, then the MOD function is called to keep the result in the

5 Visualising seasonal-diurnal wind trends Weather April 2, Vol. No. 4 Figure. Worksheet D : smoothing to remove odd/even bias. range. (Note: in Excel the $ signs lock the row or column so that this formula can be copied down the whole column.) Figures show the key features of the wind direction worksheet D. For compactness, each figure shows only the four corners of each table, with the missing rows and columns indicated by the blue lines. Figure shows how the frequency tables are compiled. Cell E5 is selected in order to show its formula, which uses the CountIfs() function to count only those observations corresponding to the wind direction in E$4, the month in $B5 and the hour in $E. The observed sectors are the rows from 1 to 3, and each row sums to the total number of observations, n, for each month and hour. The values for, required for plotting the charts, are a copy of the 3 column, and are excluded from the sum. Figure shows the conversion from counts to probability density, p, with the cell E2 selected in order to display the formula, which acts on the value of E5 in Figure. The units for p are degrees 1, hence the count for each month-hour is divided by n and by 1 (corresponding to the width of the sector in degrees). Accordingly, each row sums to the value.1. Figure shows the smoothing function used to remove odd/even bias between adjacent sectors: cell E5 is selected in order to show the formula, which takes half the value for the sector plus a quarter of the values from the sectors either side. This formula corresponds to the middle of the table, where values exist in the sectors on either side. At the left- and right-hand edges of the table it must be modified to wrap around from 3 to 1 in the proper manner. Note that the rows and columns of each table are summed, not just to obtain the required values for n, but also as checksums to ensure that no observations have been missed in accumulating the counts. The wind-speed worksheet, V, follows the same format. The tabulated values in Figure are those required by the Excel colour contour plot option for the seasonal-diurnal charts. There is no control in Excel for varying the proportions of this type of chart, each data value is plotted as a coloured square, and the resulting charts are very wide and thin: 2 by 3 for the wind direction. To improve the visual presentation, the height of each chart was doubled by interpolating additional values half-way between the observed wind-speed and direction values. Concluding remarks Data from three anemograph stations have been used to demonstrate the effectiveness of the proposed chart format in revealing seasonal-diurnal trends in wind observations. For example, the two UK stations show distinctly different diurnal characteristics associated with the respective coastal and inland locations. More detail is apparent in these charts than has been possible to discuss in the paper: for example, the rarity of southeasterly winds in mid-summer at both the UK stations. Obviously, this proposed chart format is not confined to wind observations: all other meteorological parameters that may have seasonal and diurnal trends can be presented in the same manner. The hope is that this graphical format may prove to be a useful addition to the available set of analysis tools for its ability to reveal seasonal-diurnal trends. References Cook NJ. 2. The atmospheric tide and the sea land breeze cycle in Jersey. Weather : 4. Shellard HC. 1. Tables of Surface Wind Speed and Direction Over the United Kingdom. HMSO: London, p. Correspondence to: Nicholas J. Cook njcook@ntlworld.com 2 Royal Meteorological Society doi:1.12/wea.5 1

3. EXCEL FORMULAS & TABLES

Fall 2017 CS130 - Excel Formulas & Tables 1 3. EXCEL FORMULAS & TABLES Fall 2017 Fall 2017 CS130 - Excel Formulas & Tables 2 Cell References Absolute reference - refer to cells by their fixed position.