Air Fronts

Posted on April 23, 2008 by Rashid Faridi

Fonts

the boundaries between air masses A front is defined as the transition zone between two air masses of different density. Fronts extend not only in the horizontal direction, but in the vertical as well. Therefore, when referring to the frontal surface (or frontal zone), we referring to both the horizontal and vertical components of the front.

Stationary Front

A front that is not moving When a warm or cold front stops moving, it becomes a stationary front. Once this boundary resumes its forward motion, it once again becomes a warm front or cold front. A stationary front is represented by alternating blue and red lines with blue triangles pointing towards the warmer air and red semicircles pointing towards the colder air.

A noticeable temperature change and/or shift in wind direction is commonly observed when crossing from one side of a stationary front to the other.


Image by: WXP PurdueIn the map above, temperatures south of the stationary front were in the 50’s and 60’s with winds generally from the southeast. However, north of the stationary front, temperatures were in the 40’s while the winds had shifted around to the northeast. Cyclones migrating along a stationary front can dump heavy amounts of precipitation, resulting in significant flooding along the front.

Cold Front

is transition zone from warm air to cold air A cold front is defined as the transition zone where a cold air mass is replacing a warmer air mass. Cold fronts generally move from northwest to southeast. The air behind a cold front is noticeably colder and drier than the air ahead of it. When a cold front passes through, temperatures can drop more than 15 degrees within the first hour.

Symbolically, a cold front is represented by a solid line with triangles along the front pointing towards the warmer air and in the direction of movement. On colored weather maps, a cold front is drawn with a solid blue line.

 

Warm Front

transition zone from cold air to warm air A warm front is defined as the transition zone where a warm air mass is replacing a cold air mass. Warm fronts generally move from southwest to northeast and the air behind a warm front is warmer and more moist than the air ahead of it. When a warm front passes through, the air becomes noticeably warmer and more humid than it was before.

Symbolically, a warm front is represented by a solid line with semicircles pointing towards the colder air and in the direction of movement. On colored weather maps, a warm front is drawn with a solid red line.

There is typically a noticeable temperature change from one side of the warm front to the other. In the map of surface temperatures below, the station north of the front reported a temperature of 53 degrees Fahrenheit while a short distance behind the front, the temperature increased to 71 degrees. An abrupt temperature change over a short distance is a good indication that a front is located somewhere in between.

Occluded Front

when a cold front overtakes a warm front A developing cyclone typically has a preceding warm front (the leading edge of a warm moist air mass) and a faster moving cold front (the leading edge of a colder drier air mass wrapping around the storm). North of the warm front is a mass of cooler air that was in place before the storm even entered the region.

As the storm intensifies, the cold front rotates around the storm and catches the warm front. This forms an occluded front, which is the boundary that separates the new cold air mass (to the west) from the older cool air mass already in place north of the warm front. Symbolically, an occluded front is represented by a solid line with alternating triangles and circles pointing the direction the front is moving. On colored weather maps, an occluded front is drawn with a solid purple line.

Changes in temperature, dew point temperature, and wind direction can occur with the passage of an occluded front. In the map below, temperatures ahead (east of) the front were reported in the low 40’s while temperatures behind (west of) the front were in the 20’s and 30’s. The lower dew point temperatures behind the front indicate the presence of drier air.

Dry Line

a moisture boundary A dry line is a boundary that separates a moist air mass from a dry air mass. Also called a “Dew Point Front”, sharp changes in dew point temperature can be observed across a dry line. Dry lines are most commonly found just east of the Rocky Mountains, separating a warm moist air mass to the east from a hot dry air mass to the west.

States like Texas, New Mexico, Oklahoma, Kansas, and Nebraska frequently experience dry lines in the spring and summer. Dry lines are extremely rare east of the Mississippi River.


Image by: WXP Purdue Dew points east (ahead) of the dry line shown above range from the upper 50’s to low 70’s with winds from the southeast. West of the dry line, dew points were in the 20’s and 30’s, a decrease of nearly 50 degrees. Air temperatures ahead of the dry line were generally in the 70’s and 80’s while behind the dry line, temperatures ranged from the mid 80’s to mid 90’s. Drier air behind dry lines lifts the moist air ahead of it, triggering the development of thunderstorms along and ahead of the dry line (similar to cold fronts). It is not uncommon for tornadic supercells to develop along a dry line.

dig deeper

Posted in Environment | 2 Comments

Mansoon

Posted on April 22, 2008 by Rashid Faridi

The “Monsoon”, from the Arabic “mauism” meaning “season”, defines a wind that changes direction with the seasons. Monsoons develop as a result of changing patterns of atmospheric pressure caused by the varied heating and cooling rates of continental landmasses and oceans. The strongest and most well known monsoons are those which affect India and Southeast Asia. The summer monsoon, which blows southwesterly across the Indian Ocean, is extremely wet. The winter monsoon, in contrast, blows northeasterly and is generally dry.

During May and June of each year, the summer monsoon arrives with persistent southerly wind flow driven by a warm air mass with low pressure at the surface that forms over southern Asia as it is warmed by the sun. Air from the relatively higher pressure air mass over the Indian and tropical western Pacific Ocean flows northward toward the low pressure over land, bring with it torrential rains. A late arrival of the monsoon can be bad for agriculture, as the monsoon rains are necessary for summer crops.

In India, the dry northerly wind flow over India changes direction, and warm humid air from the Indian Ocean flows from the south, gradually overspreading the Indian subcontinent. Widespread torrential rains, and even severe thunderstorms, large hail and tornadoes can accompany the onset of the summer monsoon.

The Indian Ocean version of the hurricane, which is traditionally called a “cyclone” in the Indian Ocean, can also form and move ashore in association with the onset of the monsoon. These cyclones have at times killed many thousands of poor people who live in the low-lying areas along the eastern coast of India and Bangladesh.

A weaker and much more localized monsoon occurs over the normally dry southwestern United States in the late summer when more humid air, accompanied by thunderstorms, overspreads the region.

India and Southeast Asia lie in between the centres of the tropical and subtropical climate zones. For much of the year, and particularly during winter, northeast trade winds blow across the region, from subtropical high pressure to equatorial low pressure. These winds originate from the continental interiors and are generally dry. During the summer months however, the large landmasses of Asia and the Indian subcontinent heat up, generating a seasonal continental region of low pressure. Airflow reverses and wind blows southwesterly across the Indian Ocean, accumulating considerable moisture which is deposited as heavy rainfall during the wet season from May to September.

Scientists have linked the development of the monsoonal wind phenomenon over India during Earth History to the uplift of the Himalayas and the Tibetan Plateau, which occurred about 20 million years ago when India collided into the Asian continent.

Source(s) and Link(s):

source:http://www.ace.mmu.ac.uk

Weather Questions

https://rashidfaridi.com/2008/03/06/natural-disasters-cyclones/

Frontal or Cyclonic Rains

 

 

Posted in Environment | 2 Comments

Mercator’s Projection

Posted on April 22, 2008 by Rashid Faridi

The Mercator projection was invented by Gerardus Mercator, a Flemish mapmaker. His name is a latinized version of Gerhard Kramer.

This is his famous world map of 1569.

A modern Mercator projection map

The property of the Mercator projection map that made it useful to navigators is that it preserves angles. Lines of constant compass heading (called rhumb lines by sailors) are straight lines on this map. Say you’re in Vancouver and want to get to Honolulu, Hawaii. You don’t have GPS, just a compass.

Just draw a straight line on the map between where you are and where you want to go, and measure the angle (almost exactly 45 degrees in this case). So (after a small detour around Vancouver Island) you head southwest, and off you go. If you keep heading in this direction, you ought to get there.

Earlier maps were drawn on a simple grid: each degree of latitude or longitude is the same size. This method wouldn’t work there: rhumb lines would be curves. Mercator knew that to give his map this desirable property, he had to make the lines of latitude farther apart as you go away from the equator. But he didn’t say exactly how he did it. He almost certainly didn’t have a formula, but might have done it using approximate measurements on a globe. He just said

It is for these reasons that we have progressively increased the degrees of latitude towards each pole in proportion to the lengthening of the parallels with reference to the equator.

How NOT to do it

 

Many people have an incorrect idea of how Mercator’s projection works. This seems to be commonly taught in high schools. The idea is to imagine a cylinder with the globe inside, and light projected from the centre through the globe onto the cylinder, as in the picture here. Then unroll the cylinder. This cylindrical projection is NOT Mercator’s projection.

If you want a physical model of Mercator’s projection, let the globe be a spherical balloon that is blown up inside the cylinder, and sticks to the cylinder when it comes into contact with it.

How to do it

In 1599 the English mathematician Edward Wright explained the mathematics of exactly how Mercator’s projection should be done. Let’s say that the distance on Mercator’s map from the equator to the parallel at latitude $\theta$ is $F(\theta)$, in units where the equator has length $2 \pi$ on the map.

Here is a picture of the Earth with the top sliced off at latitude $\theta$. The equator is a circle with radius $R$ (the radius of the Earth) and circumference $2 \pi R$, and the parallel at latitude $\theta$ is a circle of radius $R \cos (\theta)$ and circumference $2 \pi R \cos (\theta)$. But on the map the parallels are all the same length. So the parallel at latitude $\theta$ is stretched by a factor $1/\cos (\theta) = \sec (\theta)$. Now imagine a very small square piece of land at latitude $\theta$, with sides of length $h R$ oriented north-south and east-west. To go from its northeast corner to its southwest corner, you travel southwest. In order for Mercator’s projection to work, this has to be true for its image on the map as well: so its image on Mercator’s map must be a square. It takes up a fraction $\displaystyle \frac{hR }{2 \pi R \cos (\theta)}$ of the parallel at latitude $\theta$, so its width on the map is $ \displaystyle \frac{hR }{2 \pi R \cos (\theta)} 2 \pi = h \sec (\theta)$. So its height on the map must also be $h \sec (\theta)$. Now really the piece of land isn’t all at exactly the same latitude, it goes from $\theta$ to $\theta + \Delta \theta$ say, where the side is $h R = R \Delta \theta$, i.e. $h = \Delta \theta$. And the formula for the height on the map is approximate. So the height on the map, which is $\Delta F = F(\theta + \Delta \theta) - F(\theta)$, is approximately $\sec (\theta) \Delta \theta$. Thus $\displaystyle \frac{\Delta F}{\Delta \theta} \approx \sec(\theta)$. In the limit as $\Delta \theta \to 0$, we get $\displaystyle \frac{dF}{d\theta} = \sec(\theta)$. Thus $F(\theta)$ is an antiderivative of $\sec(\theta)$. Taking the equator as height 0, so $F(0)=0$, we can write it as a definite integral:

\begin{displaymath}F(\theta) = \int_0^\theta \sec(t) \, dt \end{displaymath}

That’s not quite the language Wright uses (this was before the invention of calculus), but it amounts to the same thing.

Well, now the problem is to do the integration. Wright didn’t know how. In fact, he didn’t know about logarithms yet, and as we’ll see we need logarithms to write down the answer. So what Wright did was to do the integration approximately, using sums (like the left or right sums we did earlier) with an interval of 1 minute of arc = 1/60 degree, for all latitudes up to 75 degrees. It must have taken a lot of effort back in those days. His table was published, and was quite useful for mapmakers.

In 1614 John Napier invented logarithms, and they were soon found to be quite useful in calculations. So useful that not only tables of logarithms, but tables of logarithms of trigonometric functions, were published, including in 1620 a table of logarithms of tangents.

In the 1640’s a man by the name of Henry Bond happened to be looking at two tables at the same time: Wright’s table of $F(\theta)$ and a table of logarithms of tangents. He noticed a coincidence: $F(\theta)$ seemed to be the same as $\ln(\tan(\theta/2 + \pi/4))$. He published this as a conjecture in 1645:

\begin{displaymath}\int_0^\theta \sec(t)\, dt = \ln\left(\tan\left(\frac{\theta}{2} + \frac{\pi}{4}\right)\right)\end{displaymath}

Nowadays, all you would have to do to verify this is note that they agree at $\theta = 0$ and differentiate:

\begin{displaymath}\,\vcenter{\openup.7ex\mathsurround=0pt \ialign{\strut\hfil... ...{2}\right)} = \frac{1}{\cos(\theta)} = \sec(\theta)\cr\crcr}}\,\end{displaymath}

But this was still before Calculus, so they couldn’t do it that way. The problem actually became one of the famous open problems of the mid-17th century. Nicolaus Mercator (no relation to Gerardus) actually offered a prize for the solution. The problem was eventually solved in 1668 by James Gregory, but his proof was extremely complicated. A more intelligible proof was published by Isaac Barrow in 1670.

source:http://www.math.ubc.ca

Posted in Geographers, Geography Practicals/Lab and Statistical Techniques, map making, oceans | 3 Comments

Prevailing Winds

Posted on April 22, 2008 by Rashid Faridi


The direction of wind is measured in terms of where the air is coming from. A northerly wind blows air from north to south. A southwesterly wind blows air from the southwest to the northeast.

The prevailing wind is the wind that blows most frequently across a particularly region. Different regions on Earth have different prevailing wind directions which are dependent upon the nature of the general circulation of the atmosphere and the latitudinal wind zones.

In general, the following prevailing winds across the Earth may be identified, although variations arise due to the positions and differential heating rates of the continents and oceans.

Latitude

Direction

Common Name

90-60°N

NE

Polar Easterlies

60-30°N

SW

Southwest Antitrades

30-0°N

NE

Northeast Trades

0-30°S

SE

Southeast Trades

30-60°S

NW

Roaring Forties

90-60°S

SE

Polar Easterlies

Wind generally blows from high pressure to low pressure, but does not take the most direct north-south route between the pressure belts on account of the Earth’s rotation, which deflects airflow by means of the Coriolis force.

The British Isles lie at the convergence zone between the warm southwest antitrades and the cold polar easterlies. Convergence of warm and cold air masses at this latitude produces cyclonic low pressure and the development of rain-bearing depressions, whish sweep across the Atlantic to influence the British climate. The prevailing winds are the mild southwesterlies, but for much of the time, the British Isles are influenced by polar air masses with a northwesterly or northerly airflow, that bring with them colder showery weather.

Prevailing winds in the Indian Oceans are northeasterly. During the summer months however, a larger low-pressure system develops over southern Asia due to continental heating. Winds in this region now reverse to form the Southwest Monsoons, which bring a prolonged wet season to Southeast Asia and the subcontinent.

read more

Posted in Environment | 1 Comment