Web Mercator is different than Mercator projection

The use of mobile apps and online maps is increasing. Everybody has access to and uses online map services such as google maps, street view or ESRI online maps. However, very often when GIS professionals use such maps as base for geo-referencing data, they forget that it uses a different coordinate system. Besides, this is a new coordinate system that sometimes has different names; this led to some confusions.

This new reference system is the so-called Web Mercator or Pseudo Mercator or EPSG3857. Many people wonder what's the difference? and why a Feature class using a Mercator projection changes when transformed into Web Mercator?

What is the difference?

A first and simple difference is that they have different false Easting and false Northing data. However, that is not the main difference. A standard Mercator projection is cylindrical conformal projection. I stress the word conformal because it is a key feature that made this projection so popular and the big difference with the Web Mercator. A conformal projection as defined by J Snyder means that the shape of every small feature of the map is shown correctly, the relative angles at each point are correct, and the local scale in every direction around any one point is constant. Thus, it preserves shapes and angles. On the other hand, Web Mercator is not conformal.

Fig 1. Conceptual difference between spherical and ellipsoid projections

Why Web Mercator is not a conformal projection?

Although Web Mercator and Standard Mercator use the same equations, they are based on different shapes. Standard Mercator assumes an ellipsoid, while Web Mercator assumes a sphere. Thus, there are differences that should be corrected by a scale factor. However, including such correction would be computationally expensive. Web Mercator is used online and requires simple equations. Otherwise, the visualization would be slow. Thus, they neglected such corrections.

The differences are function of the latitude. Latitudes closer to the equator have small errors, and the error increases as the latitude distances from the equator. The shape error in most populated areas (less than 50 degrees latitude) are small and negligible for a general visualization purposes; the computational cost of correcting such differences would be too high for such little differences. However, if detailed measurements are required, the errors would become important.

Fig 2. Error of Web Mercator projection

Tropical storms: Hurricanes, Typhoon, Clycones

Last week the Caribean islands, America and Gulf of Mexico experienced 3 Hurricanes in a row. At the same time, important Typhoons are developing on the Asia-Pacific region.

Basically, the three terms are the same. They all are tropical storms caused by the same reasons. Moist over the warm tropical ocean rises causes a low pressure area. Surrounding air pushes into this lower pressure area; thus, this air warms and rises. As this warm air rises, it cools forming cliuds and rain. Because of the Coriolis force this whole system of air, cloud, rain and wind beging spinning and growing.

Fig1. Formation of a tropical storm

The only difference between Hurricanes, typhoons and Cyclones is the local name they receive in different regions. 

Fig 2. Tropical storms different names

Tropical storms in the American region (Atlantic Ocean and America-Pacific) are known as Hurricanes. The word originates from the Mayan storm god Hunraken. Mayan people and other people from the region used the word to describes the stroms that were though to be a punishment from the god Hunraken

Tropical storms in the Asia-Pacific region are called Typhoons. In 1560 the Portuguese sailor Pinto made the first description of this tropical storm by using the word tufao. Tufao derives from the Chinese words tung (east) fung (wind). Chinese used these words to describe the strong windy storms coming from the East.

Cyclones are tropical storms on the Indian ocean. The first reference to this word is from the British sailor Piddington. The word originates from the Greek words kyklon (moving in a circle).
Strongest Tropical storms

Tropical are classified into 5 categories based on their wind speeds.
Category Wind speed [mph]
1 74-95
2 96-110
3 111-129
4 130-156
5 >156

Strongest tropical storms

Storm Year Winds [km/h] Wind [mph] Location
Patricia 2015 345 214 South of Mexico
Allen 1980 305 189 Caribean, North of Mexico
Irma 2017 295 183 Caribean, Florida
Wilma 2005 295 183 Gulf of mexico
Linda 1997 295 183 South of Mexico

Intercontinental Ballistic Missiles

During the last months we heard (and read) a lot of news about ballistic missiles and potential threads of North Korea testing Intercontinental Ballistic Missiles (ICBM). But what is an intercontinental ballistic missile and why does it pose such a threat?
First, it is important to understand what a ballistic missile is. Basically, there are 2 types of missiles: ballistic missile and cruise missiles (will be explained in another post).
A ballistic missile is a missile that follows a ballistic trajectory; that is, the path that any given thrown object (or projectile) without propulsion would take under the action of gravity. A theoretical perfect projectile trajectory only considers gravity but real projectiles also consider additional forces such as friction due to aerodynamic drag (Figure 1).
Fig 1. Ballistic trajectory

The flight of a ballistic missile has 3 phases: A first phase is a powered flight (launching); in long range missile the launching requires enough force so that the missile escapes the atmosphere. The second phase which is the longest phase is the free flight (a ballistic projectile). Usually, this second phase is outside of the atmosphere; hence, the missile has less friction. The third phase is the re-entry phase.
Ballistic missiles can be divided in four groups based on their range (Figure 2):
Short range ballistic missile. This missiles have a range between 300 km to 1000 km and may reach their target in less than 10 min.
Medium range. This missiles have a range between 1000 km and 3500 km and may reach their target in between 10 min to 15 min.
Intermediate range. This missiles have a range between 3500 km and 5000 km and may reach their target in between 15 min to 20 min.
Intercontinental range. This missiles have a range greater than 5000 km (up to 13000 km) and may reach their target in between 20 min to 30 min.
Fig 2. Range of ballistic missiles if launched from North Korea

The thread
ICBM are big threat to world's peace because of 2 factors: their range and short time to reach their target.
Range. Ballistic missiles flying above the atmosphere have a range much longer than any other missile. ICBM may easily reach target distances about 10000 km.  That is, a missile launched from North Korea may reach any European capital, any Asian city, Australia or even some major American cities such as Seattle, Los Angeles, Las Vegas or Houston.
Time to target. ICBM may reach velocities about 5 km/s and may require only 30 min to travel up to 10000 km. That is, any of the previously mentioned cities could be destroyed in just 30 min after the launch is detected. With such a short time, there would be no option to evacuate or to appropriate shelter. Thus, ICBM are lethal.

Fig 3. Ballistic missiles

This short introduction to ICBM clearly illustrates their potential as destructive lethal mass destruction weapons. Although America is developing-testing a missile defensive system, ICBM are still a threat