Dear Robert,

As I understand, you consider the variability of the rainfall during the wet days. Generally, climatic relations and dynamic meteorology describe somewhat different scales of the atmospheric processes. I think dynamic meteorology can cover broader spectrum of the atmospheric motions. So these approaches by their definition may create problems for their appropriate comparison.

It is widely known that there is an often found relationship between the variability and the value of the variable (e.g., precipitation amount): the greater variable (precipitation amount) causes the greater variability of the variable itself (precipitation amount).

It is known that the great amount of intra-day precipitation (heavy intensive precipitation) is closely related to thunderstorm activity. I think that higher rainfall concentration (i.e. precipitation variability) is highly correlated with the thunderstorm activity in the regions of interest. Perhaps you can find better logical explanation in comparing rainfall concentration with the number of thunderstorms. Or the answer can be found through the comparison of the mean daily precipitation (divided by the number of wet days) for different sites of interest.

I can mention my favourite example of the explanation for the above relationships given by dynamic meteorology. This example is related to upper troughs (an upper trough is any elongated area of low geopotential heights in the upper troposphere).

The orientation of the upper trough axis has been shown by Macdonald (1976) and Glickman et al. (1977) to correlate with the incidence of thunderstorm activity (these articles are attached to the message).

1) Negative tilt. When the axis of a trough extends northwest-southeast in the Northern Hemisphere (southwest-northeast in the Southern Hemisphere), a negative-tilt trough is described. This correlates with a higher incidence of widespread thunderstorms and with larger precipitation amounts. Negative-tilt troughs are not as common as positive-tilt troughs.

2) Positive tilt. When the axis of a trough extends northeast-southwest in the Northern Hemisphere (southeast-northwest in the Southern Hemisphere), a positive-tilt trough is described. This correlates with a lower incidence of widespread thunderstorms. Positive-tilt troughs are more common than negative-tilt troughs.

Shortly, you can pick some statistics about the trough occurrences and their tilt occurrences. Perhaps such datasets can explain certain issues with rainfall concentration for different sites.

Sincerely,

Oleksandr.

Dear Robert,

I can advice you to look at the following official document:

WMO-No. 1045 (Manual on Estimation of Probable Maximum Precipitation (PMP)) published in 2009. The link is attached below (PDF file is very huge).

You can find many explanations and examples on your topic. You mentioned about explanations in dynamic meteorology for possible relationships between the number of wet days and the rainfall concentration.

I can give some interest fragments from WMO-No. 1045.

1) Chapter 5.4.2 (p. 126):

"Basic to any procedure for using data from another

region of the world is a comparison of the meteorology

of storms in the different regions and their

depth–area–duration characteristics. In each region

considered here, extreme rainfall amounts for short

durations and small areas will be produced by large,

efficient and virtually stationary thunderstorms, or

by part of a meso-scale or synoptic-scale storm

system with embedded cumulonimbus cells. The

precipitation is considered to be a function of the

available moisture and a convergence factor."

So, the convergence factor is one of the examples given by dynamic meteorology to explain high rainfall concentration in certain regions.

* Convergence is a horizontal shrinking and vertical

stretching of a volume of air, accompanied by net

inflow horizontally and internal upward motion.

2) Chapter 2.10.4 (p. 28):

"In those regions where summers are dry and major

storms occur only in the cold half of the year, the

seasonal variation of maximum precipitable water

(section 2.10.3) gives a false indication of the

seasonal variation of PMP when used alone. A wind

factor is also required to develop a representative

seasonal variation of PMP.

Figure 2.13 shows a seasonal variation curve developed

for PMP in the Upper Tigris River basin, where

in summer there is very little rain. While the maximum

dewpoint and precipitable water curves tend

to show minimum values during the cold season,

climatological records show that in this region all

major general-type storms occur in that season.

Weather charts indicate that the heaviest precipitation

occurs with surface winds in the south-eastern

and south-western quadrants. A survey of a long

record of surface winds yielded the maximum

24-hour wind curve in Figure 2.13, part C, which

shows peak values in January and February. Multiplication

of precipitable water values by wind speed

resulted in the moisture-inflow index curve shown

in part D. The double peak was confirmed by

outstanding recorded storms."

This fragment considers one interesting example explaining the role of the wind factor in seasonal variations of high rainfalls (explanations given by dynamic meteorology). This fragment is also attached as an image file containing the block of text and the appropriate figure (for your convenience).

Sincerely,

Oleksandr.

http://library.wmo.int/opac/index.php?lvl=notice_display&id=1302#.VXALukom9Ft

Dear Oleksandr

Thanks for your answer. What you mention is true, but I was referring to a more general relationship between the number of rainy days and the distribution of rainfall in those days (see CI of Martin-Vide, 2004).

Indeed, it is expected that areas with more storms present a more uneven distribution of rainfall in the year; but there are exceptions. For example, Brazil has a large number of days of rain and thunderstorm, but its distribution is more regular (lower CI) than in the Sahara and Arabia. However, in Brazil the correlation between wet days (WD) and the concentration index is positive (CI is higher for the wettest areas), while in Saudi is negative, like much of Europe and Asia.

Martin-Vide and I are preparing a paper on these issues. I'll see if I can upload a pre-print for you read it. Meanwhile I attached a provisional map of the spatial distribution of the correlation between WD and GI (empirical version of CI).

Best regards,

Robert

http://onlinelibrary.wiley.com/doi/10.1002/joc.1030/abstract

http://www.nat-hazards-earth-syst-sci.net/12/2799/2012/nhess-12-2799-2012.pdf

Dear Ansar,

I think you have kept the previous answer (Oleksandr).

Dear Oleksandr,

Thanks for your two answers. I had forgotten to add an extra comment.. We have also analyzed the possible relationship between the number of days of thunderstorm and rain concentration (CI). Unfortunately there are few data about the fraction (relative value) of stormy days on rainy days, especially in areas of Africa. In addition, there are areas "without" storms (e.g. Eastern Sahara), but with a greater rainfall concentration (in its very few rainy days). And regions as Brazil present a low CI but its number of stormy days is very high.

However we have found a clearer relationship between convection and rain concentration of intra-daily scale. I recommend reading about the index n: https://www.researchgate.net/publication/237786777

Best regards,

Robert

http://i.imgur.com/2kqiPv8.gif

http://electrical-engineering-portal.com/wp-content/uploads/world-number-thunderstorm-days-per-year.gif

http://upload.wikimedia.org/wikipedia/commons/9/95/Global_Lightning_Frequency.png

http://www.inforse.org/europe/dieret/Solar/asolarirrad.gif

Article Climatic study of the exponent “n” in IDF curves: applicatio...

Dear Robert,

The problem of any statistical approach is hidden in its assumption of idealistic random character of the physical process considered. Sometimes, when such process is highly determined by some strong physical law, statistic results can disappoint. I think that some funny maxim for any statistical instrument can be applied: “If from all available instruments (of problem solving) you have got a hammer only, then every problem considered by you turns into a nail.”

You say:

“Indeed, it is expected that areas with more storms present a more uneven distribution of rainfall in the year; but there are exceptions. For example, Brazil has a large number of days of rain and thunderstorm, but its distribution is more regular (lower CI) than in the Sahara and Arabia.”

By this sentence you want to compare precipitation rainfall in very different regions (Brazil with high lightning frequency versus – Sahara and Arabia with low lightning frequency) as a completely random process by the same measure CI (“hammer” tool). Brazil has a quite different type of climate (most of the country is tropical) comparing to Sahara and Arabia (arid climate). It causes different precipitation nature, circulation factors, and rainfall distribution.

As I think, Brazil is an example of “the excerption” that even makes the “rule” more proved. If our assumption about random precipitation pattern in Brazil is wrong? Thunderstorms are highly sudden in temperate latitudes (with varying rainfalls which are generally separated from each other in time by dry days), but in tropics they can have a highly organized persistent nature. Let us assume we have an ordinary Brazil station with 60-100 thunderstorm days per year. There can be a dry season and a wet season. The prevailing part of the precipitation falls during the wet season. Let’s think that due to thunderstorms it rains every day (throughout wet season), and the amount of daily rainfall is high but always the same (nothing changes from day to day after wet season has established – there are no atmospheric fronts’ activity and air masses’ outbreaks). Of course, it is a kind of idealization. So, showers, which are highly irregular (for temperate latitudes), become a part of a highly regular pattern (on a daily basis). It will result in a low variability and a low CI value (and the small amounts of more chaotic rainfalls during the dry season will not be capable to significantly increase general precipitation variability).

Sincerely,

Oleksandr.

Dear Robert,

Let me make further assumptions about Brazil. All my statements must be considered as jokes of imagination (without clear mathematical proof).

You say:

“However, in Brazil the correlation between wet days (WD) and the concentration index is positive (CI is higher for the wettest areas), while in Saudi is negative, like much of Europe and Asia.”

I think that the main reason for “Brazil anomaly” is closely related to the existing limit of days (total – 365 per year). The entire statistic system changes its behavior, because there are limits for the growth of its main parameters. One of the dialectics' laws states that at the critical moment the growing quantity can cause not only the parameters’ gradual increase of the system, but apply quality changes to the whole system. It looks like system becomes saturated, and further hypothetical processes will follow completely different trajectories.

The number of wet days in Brazil exceeds 200 (more than half of the year). Brazil looks like a globe leader for its wet days. So, you can’t simply increase its wet days infinitely. The system will make some important response to such actions.

High amounts of daily “almost constant” rainfall occur every day during the wet period. There are no days without rain in the wet period. What is the way for increasing wet days’ number (when considering relationships between the number of wet days and the rainfall concentration)?

I think that the increasing number of wet days in Brazil will be related to gradual decreasing of the dry period and filling it with wet days (but with smaller rainfalls compared to the existing “major” wet period). The total number of cases for “more chaotic” relatively small rainfalls during the dry season will grow, affecting CI and increasing it together with overall precipitation variability.

Sincerely,

Oleksandr.

Dear Oleksandr,

I totally agree with what you say. In fact your hypothesis coindicen with what I thought. But just in case, the question has been shared to see if more people thought similarly.

You say:

"I think that the increasing number of wet days in Brazil will be related to gradual decreasing of the dry period and filling it with wet days (but with smaller rainfalls compared to the existing “major” wet period). The total number of cases for “more chaotic” relatively small rainfalls during the dry season will grow, affecting CI and increasing it together with overall precipitation variability".

I think that's the key. Thanks!

Regards,

Robert

Dear colleagues

It is a pleasure to present these two papers relating to the question:

https://www.researchgate.net/publication/290648537

https://www.researchgate.net/publication/284913248

Best regards,

Robert

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