Decadal and Inter-decadal changes in rainfall: III.

Summer rainfall anomalies and trends

Part 3 of 3: A growth and collapse model for summer rainfall

(See Notes below for data and plotting details.)

A linear trend

In Part II, I showed that a linear trend fits well (R-squared = 0.54) to smoothed summer rainfall at Manilla, NSW from 1897 to 1976. This trend-line rises extremely steeply: 156 mm per century.
(See also the Duodecadal Means graph below.)

Implications of the extreme trend

Such an extreme trend cannot extend more than a short time into the past or the future without reaching physical limits. Extremely high values must be followed by lower values and vice versa. The oscillation between higher and lower values in nature is often modeled as a smooth harmonic curve. That does not fit well here. Not only does the rise from 1897 to 1976 fail to curve down approaching the final peak, the falls from 1892 to 1900 and from 1975 to 1987 are extremely sharp. They are collapses.
It seems to me that a model of steady growth followed by sudden collapse may perhaps reflect the processes involved. On the graph I have added speculative trend lines of the same rising slope as that observed for 1897 to 1976. The constant for the first speculative trend line is 130 mm higher and leads to a 130 mm collapse from 1896 to 1899. A 90 mm collapse from 1978 to 1981 then leads to a renewed rising trend that is 90 mm lower.


 Duodecadal Means

To express this progressive rise in summer rainfall (1897-1976) differently, I add the graph below. Reports on global warming commonly use graphs showing that each decade’s average value is higher than the one before. Here, I have calculated duodecadal summer rainfall averages from the raw data. It is clear that each 20-year period is much wetter than the one before. In fact, the rise from one duodecade to the next increases: first 15 mm, then 31 mm, and 49 mm. (Decade averages are not shown, as each second value steps down.)

 Log of smoothed summer rainfall anomaly and duodecadal means


Notes

Rainfall at Manilla, NSW, has been observed since 1883. As I posted earlier, there are two distinct rainfall modes, centred on the summer and winter solstices. The summer (monsoon) mode has nearly twice the rainfall of the winter (westerly) mode.

Here, I have assigned to the winter mode the monthly data from April to September, and assigned to the summer mode the monthly data from October, extending to March in the following year.
Each data value has been expressed as an anomaly from the 130-year mean. I found the anomalies not only for the “summer” and “winter” totals, but also for their sum (April to March) and their difference (summer minus winter). To remove high-frequency noise and the effect of ENSO from the plotting, I applied a Gaussian filter of half-width 6 years.

Decadal and Inter-decadal changes in rainfall: II.

Log of smoothed summer and winter rainfall anomalies.

Part 2 of 3: The record restricted to 1891-1982 (92 years)

(See Notes below for data and plotting details.)

No climatic record is ever long enough to demonstrate apparent cycles,trends or extremes beyond doubt. In Part 1, a linear trend of summer rainfall rising at 24.7 mm per century was fitted to the whole 130-year record. Although this is a very high (perhaps unsustainable) rate of increase, the trend line explains hardly any of the variation. The R-squared value is 0.03! However, there does seem to be a steeper quasi-linear trend prevailing for most of the period of record. The graphs I have posted here show a restricted record beginning in 1891 and ending in 1982. This simulates an analysis done in 1983 (which could not have used more recent data) and supposes that records earlier than 1891 were unavailable for some reason.

I have chosen these dates so that
(i) the near-record smoothed summer rainfall maximum of 1891 is excluded but the record smoothed summer rainfall minimum of 1900 is included;
(ii) the record smoothed summer rainfall maximum of 1975 is included but the very low smoothed summer rainfall minimum of 1987 is excluded.
(Due to the smoothing window extending six years before and after a specified date, smoothed rainfall values can be calculated only from 1897 to 1976.)

Log of smoothed sum and difference of summer and winter rainfall anomalies.

Linear trends

For this restricted data set of 92 years, all four linear trends are very much steeper than for the whole 130-year record. The R-squared values are also much higher, indicating that the trends explain much more of the variation. The R-squared values of 0.54 for summer rainfall anomaly (red)  and 0.58 for the seasonal difference anomaly (orange) are quite respectably high.
Gradients of the four trend lines are:
Smoothed summer rainfall anomaly (red) : +156 mm per century;
Smoothed winter rainfall anomaly (blue) : -53 mm per century;
Smoothed seasonal difference rainfall anomaly (orange) : +209 mm per century;
Smoothed (summer+winter) rainfall anomaly (purple) : +104 mm per century.

Average rainfall values

I showed in an earlier post that mean rainfall values were:
Summer rainfall: 420 mm (64%);
Winter rainfall: 232 mm (36%);
Summer minus winter: 188 mm;
Summer plus winter 652 mm (100%).
From the intersection of trend lines with the zero line on the graphs, these mean rainfall values were experienced about 1935.

Historic and future summer rainfall at Manilla, NSW

The linear trends imply extreme rainfall climates in the past and in the future. Extrapolating the summer linear trend at 156 mm per century gives amazing results. The summer season rainfall at Manilla would have been zero in 1666, the year of the Great Plague of London. Before that, summer rainfall would have been negative.
By the year 2200, summer rainfall can be expected to double to 840 mm , a value now mainly found in the tropical north. The inbalance between summer and winter rainfalls changes even faster than summer season rainfall.
So far, this exercise seems to show mainly the danger of linear extrapolation, as demonstrated in 1883 by Mark Twain in the case of the shortening of the Mississippi River.


Notes

Rainfall at Manilla, NSW, has been observed since 1883. As I posted earlier, there are two distinct rainfall modes, centred on the summer and winter solstices. The summer (monsoon) mode has nearly twice the rainfall of the winter (westerly) mode.

Here, I have assigned to the winter mode the monthly data from April to September, and assigned to the summer mode the monthly data from October, extending to March in the following year.
Each data value has been expressed as an anomaly from the 130-year mean. I found the anomalies not only for the “summer” and “winter” totals, but also for their sum (April to March) and their difference (summer minus winter). To remove high-frequency noise and the effect of ENSO from the plotting, I applied a Gaussian filter of half-width 6 years.

September 2014 cool and dry

Acacia decora hedge

A hedge of western golden wattle

The daily weather log

Two 5-day cool spells began on the 2nd and the 17th. Days and nights were both three or four degrees cooler than normal. At the same time, the air was very dry: a new lowest September dew point of minus 8.1° came on the 19th.
At other times, temperatures were near normal. There were four frosts (normally three). There were four rain days, which is normal.
The first thirty-degree day since mid-winter came on the 30th. At Manilla, it often comes near the spring equinox (September 22nd). In the 21st century, the first thirty-degree day came as early as August 23rd in 2009 and as late as November 9th in 2010.

Weather log September 2014.

 Comparing September months

Last September had been the warmest in this century. While not cold like September 2004, this month was half a degree cooler than normal. Like September in 2003, 2007, and 2012, it was both cool and dry. By contrast, the cool Septembers of 2010 and 2011 were wet, affected by La Nina.
Cloudiness and daily temperature range were near normal, but the mean dew point (1.4°) was not much higher than the extreme low value (0.6°) set last year.
The total rainfall of 18.8 mm is in the 26th percentile, well below the September average of 41 mm. Totals for periods of more than one month now have serious shortages for six months (7th percentile), nine months (7th percentile), and fifteen months (5th percentile), and a severe shortage for eighteen months (4th percentile).

The current drought report (6/10/2014) of the Bureau of Meteorology shows some serious and severe rainfall deficiencies in the area. Ten-month deficiencies extend west to Manilla from the Northern Tablelands, and there are 24-month rainfall deficiencies near Manilla and widespread around Walgett, 300 km to the north-west.

Climate September 2014.  


Data. Rainfall data is from Manilla Post Office, courtesy of Phil Pinch. Temperatures, including subsoil at 750 mm, and other data are from 3 Monash  Street, Manilla.

3-year trends to September 2014

Parametric plots of smoothed climate variables at Manilla
“September 2014 had little rain”

Trends to September 2014

 September data (orange)

Most raw anomaly values for September remained on the cool-moist side of normal. However. both rainfall and dew point were again well below normal.

Fully smoothed data (red)

The latest fully-smoothed data (March 2014) continued the trends established in summer. All were moving away from drought, except for daily minimum temperature. That is, nights were becoming very warm.


Note:

Fully smoothed data – Gaussian smoothing with half-width 6 months – are plotted in red, partly smoothed data uncoloured, and raw data for the last data point in orange. January data points are marked by squares.
Blue diamonds and the dashed blue rectangle show the extreme values in the fully smoothed data record since September 1999.

Normal values are based on averages for the decade from March 1999. They appear on these graphs as a turquoise (turquoise) circle at the origin (0,0). A range of anomalies called “normal” is shown by a dashed rectangle in aqua (aqua). For values in degrees, the assigned normal range is +/-0.7°; for cloudiness, +/-7%; for monthly rainfall, +/-14 mm.

 

September Climate Anomalies Log

Heat Indicators log for September months

This post is the seventh in a set for the 12 calendar months that began with March. Graphs are sixteen-year logs of the monthly mean anomaly values of nine climate variables for Manilla, NSW, with fitted trend lines. I have explained the method in notes at the foot of the page.

Raw anomaly values for September

Extreme values of September anomalies in this period were all in the “Moisture Indicators” group:

Temperature range anomaly (minus) +3.6 deg: September 2010;
Cloudy days % anomaly +33%: September 2010;
Dew Point Anomalies (4) -3.8 deg: September 2011, -4.7 deg: September 2012, -4.9 deg: September 2013, -4.1 deg: September 2014.

Trend lines for September

Heat Indicators

The trend of daily maximum temperature anomalies was concave, with a minimum at 2007. The trend of mean temperature anomalies was similar, but less concave. The trend of minimum temperature anomaly was almost straight, but had a weak maximum in 2008 and ended low. The subsoil temperature anomaly trend was parallel to that of the daily maximum, but higher.

Moisture Indicators log for September months

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Decadal and Inter-decadal changes in rainfall: I.

Log of smoothed summer and winter rainfall anomalies.

Part 1 of 3: The whole 130-year record

(See Notes below for data and plotting details.)

Anomalies of smoothed summer and winter rainfall

Episodes of high or low summer rainfall do not coincide with those of winter rainfall (except in 1891). Nor do they consistently oppose each other, although this is common. The summer rainfall anomaly (red) was extremely low (-101 mm) about 1900, and extremely high (+119 mm) about 1975. The winter rainfall anomaly (blue) had lower extreme values: 1939 (-48 mm) was the lowest of several low values, and 1987 (+63 mm) the highest of several high ones.

Seasonal sums and differences

I plotted the smoothed yearly value of rainfall anomaly as the sum (purple) of a winter anomaly value and that of the following summer. There was an extreme maximum in 1891 (+139 mm!), and minimal values in 1899 (-79 mm) and 1913 (-87 mm), among others.
The difference between summer and winter seasonal anomalies (orange) shows as an extreme summer excess in 1974 (+163 mm), and extreme winter excesses in 1900 (-126 mm) and 1987 (-114 mm).

Log of smoothed sum and difference of summer and winter rainfall anomalies.

“Dreadful Thirst”

Banjo Paterson’s comic verse “City of Dreadful Thirst” refers to the town of Narromine, 300 kilometres west of Manilla.
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Hammering Global Warming Into Line

Global temp and IPO graph

In my post of 18 Sep 2014 “The record of the IPO”, I showed a graph of the Inter-decadal Pacific Oscillation,plotted as a cumulative sum of anomalies (CUSUM). This CUSUM plot has a shape that makes it seem that it could be used to straighten the dog-leg (zig-zag) trace of global temperature that we see. A straighter trace of global warming would support the claim that a log-linear growth in carbon dioxide emissions is the main cause of the warming.

My attempt to straighten the trace depends on the surmise (or conjecture) that the angles in the global temperature record are caused by the angles in the IPO CUSUM record. That is, the climatic shifts that appear in the two records are the same shifts.
I have adopted an extremely simple model to link the records:
1. Any global temperature changes due to the Inter-decadal Pacific Oscillation are directly proportional to the anomaly. (See Note 1.);
2. Temperature changes driven by the IPO are cumulative in this time-frame.

To convert IPO CUSUM values to temperature anomalies in degrees, they must be re-scaled. By trial and error, I found that dividing the values by 160 would straighten most of the trace – the part from 1909 to 2008. (See Note 2.) The first graph shows (i) the actual HadCRUT4 smoothed global temperature trace, (ii) the re-scaled IPO CUSUM trace, and (iii) a model global temperature trace with the supposed cumulative effect of the IPO subtracted.


The second graph compares the actual and model temperature traces. I note, in a text-box, that the cooling trend of the actual trace from 1943 to 1975 has been eliminated by the use of the model.
The graph includes a linear trend fitted to the model trace for the century 1909 to 2008, with its equation: y = 0.0088x – 0.9714 and R² = 0.9715.

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