15 Atmospheric Moisture Humidity – Measurement and Distribution

Dr. Jitender Saroha

epgp books

   

 

 

Objectives

  • define humidity from different perspectives,
  • understand various measures of humidity with their advantages and disadvantages,
  • distinguish between absolute humidity, specific humidity, mixing ratio, vapour pressure, saturation and dew point temperature
  •  establish the relationship between temperature and humidity,
  •  describe the spatial and temporal variations of distribution of humidity, and;
  • describe instruments or devices used for measurement of humidity.

    Contents

 

Introduction

 

Learning Objectives

 

Humidity

 

Three States of Water

 

Hydrological Cycle

 

Humidity Measurements

 

Absolute Humidity

 

Specific Humidity

 

Mixing Ratio

 

Vapour Pressure and Saturation

 

Relative Humidity

 

Dew Point Temperature

 

Distribution of Humidity

 

Instrumental Measurements of Humidity

 

Summary and conclusions

 

Multiple Choice Questions

 

Answers:

 

References

 

Web Links

 

   Introduction

 

   You must have noticed that when we come under a running fan after having a bath with wet body, after sometime, the water from skin disappears and it becomes dry. Likewise, you must have observed that when a chilled water bottle from refrigerator is placed on table, after sometime, water droplets emerge on its surface. In the first case, due to evaporation water gets converted in gaseous i.e. water vapour and second reversal takes place. This presence of water vapour in air is known as humidity. Water is present in biosphere in all the three forms of matter and changes from one state to another activate the hydrological cycle. In this module, the focus is on gaseous form of water i.e. humidity – measurements and distribution.

 

 Learning Objectives

 

After studying this module, you will be able to:

 

Humidity

 

The general term humidity refers to the amount of water vapour present in the air. The water vapour is gaseous form of water and its share is about 2 per cent in the composition of atmosphere. The content of humidity in air varies from place to place and time to time. It ranges from almost zero in the cold and dry air of arctic regions in winter to about 5 per cent in the hot and humid equatorial region.However, the total amount of water vapour remains nearly constant.The presence of water vapour has a significant role in determining the weather conditions of a particular place. Indeed, meteorologists and climatologists have recognized water vapour as vital component of atmosphere as far understanding of atmospheric processes in concerned.

 

Presence of water in all the three forms of matter in biosphere is a unique gift of nature. Some of the several reasons of its great significance are following:

  • the quantity of water vapour present in a given volume of air indicates the precipitation potential;
  • water vapour, as primary greenhouse gas, is a regulator of terrestrial heat;
  • the presence of water vapour represents the amount of latent heat stored up in the atmosphere for the genesis of storms (cyclones)and turbulences;
  • it determines the stability and instability of air masses; and
  • the amount of water vapour also influences human efficiency and health conditions.

    Three States of Water

 

Water occurs in all the three states of matter – (i)solid, frozen as crystalline ice; (ii) liquid, as water and (iii) gaseous, as water vapour. Water is converted into gaseous form or water vapour by the process of evaporation. During evaporation heat is absorbed, in the evaporation of one gram water about 600 calories of sensible heat is converted into the latent form as the latent heat of vapourisation (the latent heat of vapourisation varies from about 600 calories per gram for water at 0C to 540 calories per gram at 100C). In the reverse process of condensation water vapour changes into liquid state or water andan equal amount of energy is released as latent heat of condensation.

 

The change from liquid state to solid is called freezing and from solid to liquid state, melting. During melting heat is absorbed (about 80 calories per gram of water) and during freezing the same amount of heat is released.This heat is referred to as the latent heat of fusion.The process of direct transformation of ice into water vapour is known as sublimation. Its reverse process is also known as sublimation or deposition or crystallization. In these transformations about 680 calories heat per gram are involved. These changes in states and accompanying exchanges of heat energy have prime significance in meteorology and climatology. These changes are represented with the help of a diagram, in which arrows show the six possible changes of states (Figure 1).

 

Figure 1: Three States of Water

Source:http://healingearth.ijep.net/sites/default/files/styles/chapter_photo_wide/public/images/fig_ 4_phase_change_rev.jpg?itok=SsfVQoHP

 

The Hydrological cycle

 

The hydrological cycle predominantly involves the three processes – evaporation, condensation and precipitation. It is a gigantic system, energized by Sun, in which the vital link between lands and oceans is provided by atmosphere. Briefly, it represents the continuous movement of water from the oceans to the atmosphere, from atmosphere to the landmasses, from landmasses back to the oceans. Therefore, hydrological cycle represents interchanges of both physical state as well as geographical positions. Indeed, the movement of water in this complex hydrological cycle holds the key for distribution of moisture over the earth surface (Figure 2). Hydrological cycle is intricately related to all weather and climatic phenomena.

 

Figure 2: The Hydrological Cycle

Source:http://nj.gov/drbc/library/images/hydrocycle2.jpg

 

Water vapour in the atmosphere is derived through evaporation from the oceans and seas, terrestrial lakes, land water bodies (tanks and ponds), rivers, and ice-fields and glaciers. These sources of moisture extend over about 75 per cent of the earth’s surface. In addition to these sources, evaporation of soil moisture, transpiration from plants and animal respiration also contribute moisture to the atmosphere. Aridity, temperature and velocity of winds are the major determinants of the amount and intensity of evaporation. The relationship is direct, which means the high aridity, high temperature and high velocity of winds indicates higher rates and amount of evaporation. Evaporation from oceans is more as compared to continents. In continental areas maximum evaporation occurs between 100N and 100 S latitudes. In case of oceans, the latitudinal zone of 100-200 latitudes in both the hemispheres records maximum evaporation.However, land-sea moisture exchanges and latitudinal moisture exchanges are common. The prevailing winds, air masses, cyclones, and other atmospheric disturbances play a very significant role in these moisture exchanges.

 

Humidity Measurements

 

As defined earlier, humidity is the general term which refers to the amount of water vapour present in the air. Several methods of measurement have been devised by scholars to express the presence of water vapour in air. The well known measurements of humidity are following:

  • absolute humidity;
  • specific humidity;
  • mixing ratio;
  • vapour pressure and saturation
  • relative humidity and
  • dew point.

    Absolute Humidity

 

Absolute humidity is the mass of water vapour in a given volume of air. It is generally expressed as grams per cubic meter of air. Movement of air from one area to another, changes in temperature and pressure and results into changes in volume due to expansion or contraction. It changes the absolute humidity, even without addition or removal of moisture i.e. even when amount of moisture remains constant. For instance, if in one cubic meter parcel of air, at surface, mass of water vapour is 10 gram, absolute humidity is 10 g/m3. If this parcel of air rises, due to decrease in pressure it expands and volume may become 2 m3, then absolute humidity in the same parcel of air becomes 5 g/m3, though there is no addition or removal of moisture.Therefore, it is difficult to monitor the water-vapour amount of a moving mass of air with the help of absolute humidity index. That is why it is not generally preferred by meteorologists.

 

Specific Humidity

 

The actual amount of moisture present in air is expressed by specific humidity. It is the ratio of mass of the water vapour to the mass of air, including water vapour. It is usually expressed as grams per kilogram of air. It is not affected by changes in pressure and temperature.To check it, let us come back to the example quoted in absolute humidity. The mass of water vapour in a parcel of air was 10 gram, if the mass of that one cubic meter of parcel of air including water vapour is one kilogram the specific humidity is 10 g/kg. Now if this parcel of air rises, its pressure and temperature change and volume also changes and even if it doubles in volume the ratio of mass of water vapour and mass of air remains constant i.e. specific humidity remains 10 g/kg, whereas the absolute humidity changed from 10 g/m3 to 5 g/m3. Similar is the situation with mixing ratio.

 

Mixing Ratio

 

It is closely related to specific humidity. It is ratio of the mass of water vapour in a unit air compared to the remaining mass of dry air.It is measured in the units of mass, usually grams per kilogram, like specific humidity. It is not affected by changes in temperature or pressure.A value of 10 gram per kilogram as mixing ratio means the total mass for the mixture is 1010 g. In case of specific humidity of 10 gram per kilogram the total mass is one kilogram. These differences in specific humidity and mixing ratio, in most situations, are insignificant. However, it is not easy to determine absolute humidity, specific humidity and mixing ration by direct sampling. Therefore, other measurements like vapour pressure, relative humidity and dew point are used to express the moisture content of air.

 

Vapour Pressure and Saturation

 

This measure of the moisture content of the air is derived from the pressure exerted by water vapour. It represents the partial pressure exerted by water vapour in the air. It is measured in the same units used for barometric pressure i.e. millibars.Like other atmospheric gases, water vapour exerts pressure.Due to evaporation, water molecules are added in the air above and it is reflected by small increase of air pressure. This increased pressure represents vapour pressure and is defined as that part of the total atmosphere pressure which is attributable to its water vapour content.However, with the passage of time as more and more molecules evaporate from the water surface, the gradually increasing vapour pressure in the air above forcesmore and more of these escaping molecules to return to the liquid. Finally at one stage, the number of water vapour molecules leaving and returning to the evaporating surface becomes same. This condition represents saturation and this time pressure is called saturated vapour pressure.The temperature of air at this time represents its dew point temperature, or frost point (if below freezing). Saturation vapour pressure varies with temperature and at temperatures below 0C it is slightly lower over ice than over liquid water. Therefore, if temperature of the air above increases than the amount of moisture required for saturation will be more (Table This table represents the amount of water vapour required for saturation of one kilogram of dry air at different temperatures.

 

Table 1: Water Vapour Capacity (at mean sea-level pressure)

 

Source: Lal, D.S. (1993), P-149

 

The Table 1 shows that the saturation vapour pressure is temperature-dependent. At higher temperatures more water vapour is required for saturation.It is noteworthy that for every 100C increase in temperature, the amount of water vapour needed for saturation almost doubles. Thus, four times more water vapour is needed to saturate one kilogram air at 250C air than at 50C. The difference between the water vapour holding capacity and actual amount of moisture present in air is known as the saturation deficit.

 

Relative Humidity

 

Relative humidity is defined as the ratio of the actual water vapour content in the air to the amount of water vapour required for saturation at that particular temperature in the same air (Figure 3). Therefore, it does not represent the actual amount of water vapour in air but shows only how far or how near the air is from saturation.It has no unit of measurement and is always expressed in percentages. For example, in the Table 1, at 200C temperature one kilogram air gets saturated when it contains 14 g of moisture. Thus, if that air has presence of 7 g water vapour, the relative humidity is expressed as 7 (actual)/14 (saturation capacity)and multiplied by 100 gives the value in percentage, or 50 per cent.

 

Figure 3: Relative Humidity

 

Source: http://www.fondriest.com/reviews/wp-content/uploads/2013/08/humidity_whatis.jpg

 

The relative humidity can be changed in two ways:

  • by addition or removal of water vapour; and
  • by change in temperature.

 

In our example, if through evaporation 7 g additional water vapour gets acquired at the same temperature (200C) by that parcel of air than relative humidity becomes 100 per cent. Likewise, relative humidity can become 100 per cent even without addition of water vapour by reducing the temperature to 100C. The air with 100 per cent relative humidity is known as saturated air. In atmosphere, the change in temperature and associated changes in relative humidity play a significant role in determining weather conditions. These changes include diurnal, seasonal and annual changes in temperature, temperature changes due to horizontal motion of air, temperature changes in fronts and temperature changes associated with the vertical movement of air.

    Relative humidity can also be expressed as the ratio of the observed vapour pressure to that required for saturation at a particular temperature. As follow:

 

RH ═ e/es

 

Where,RH stands for relative humidity, ‘e’ for vapour pressure, and ‘es’ for saturation vapour pressure. To derive values in percentage it is multiplied by 100.

 

Dew-point Temperature

 

Dew-point temperature or simply dew point is another significant measure of humidity. It represents the temperature to which air is cooled to achieve saturation. You can recall the example quoted in relative humidity, that at 200C if the water vapour content is 7 g, then the relative humidity is 50 per cent. If temperature is reduced to 100C the air becomes saturated, with 100 per cent relative humidity. Therefore, 100C is the dew point or dew-point temperature. As it is a measure of the actual moisture present in a column of air, it is better than concept of relative humidity which shows only how far or how near the air is from saturation. It is easy to determine because of its direct association to the amount of water vapour in the air. Dew-point temperature has emerged as one of the most significant measures of humidity. It is used to determine association of the amount of moisture with human comfort (Figure 4).

 

Figure 4: Dew Point Based Comfort Ranges

Source: http://wynonahweather.com/Wynonah/DewPointPIC.jpg

     It has already been concluded that the saturation vapour pressure is temperature dependent. For every 100C rise in temperature, the content of water vapour required for saturation doubles (Table 1). Thus, comparatively cold saturated air (50C) holds half the water vapour of saturated air having a temperature of 150C and one-fourth that of hot saturated air with a temperature of 250C. It shows that the low dew-point temperatures represent relatively dry air and high dew-point temperatures are indicator of moist air. Therefore, the dew-point temperature is a good measure of the amount of water vapour in the air and is commonly used in weather maps. Surface dew-point temperature (in 0F) based map of North America effectively shows the distribution of moisture over the continent (Figure 5).

 

Figure 5: Dew Point Temperature in North America

 

Distribution of Humidity

 

There are spatial and temporal variations in the distribution of humidity. These variations are common in vertical distribution as well as horizontal distribution. About half of the atmospheric moisture is concentrated below about 1450 meter and more than 90 per cent of the water vapour is below 5,575 meter. The seasonal variations in vertical distribution of humidity are mainly up to the height of 3,000 meter or so (Figure 6). It is noteworthy that the vertical concentration of humidity decreases form equator to poles (Figure 7).

 

Figure 6: Vertical Variation of Atmospheric Water Vapour

 

 

Source:http://www.goesr.gov/users/comet/tropical/textbook_2nd_edition/media/graphics/spec_humidity_profile.jpg

 

 

Figure 7: Distribution of Precipitable Atmospheric Water Vapour

Source:https://friendsofscience.org/assets/documents/FOS%20Essay/Nvap_lpw_1991.jpg

 

The mean storage of water vapour in the atmosphere is also known as the precipitable water content is about 2.5 cm. It is about 2.2 cm in January and 2.7 cm in July.The figure shows that precipitable water vapour decreases from equator to poles and the amount also decreases with height. In the first layer, which extends from surface to 700 mb i.e. up to the height of about 3 km it is in the range of about 2 mm in polar areas to about 12 mm over equator. The second layer, 700 to 500 mb means 3 km to 5.5 km height range has precipitable water with same pattern in the range of 1 to 9 mm. In the top layer, at height above 5.5 km the moisture content is limited and it is the range of 0.5 to 2 mm. Therefore, broad generalization about water vapour distribution is that it decreases with increase in altitude. The second measure generalization is that it decreases from equator to poles (Figure 8). This pattern is reflection of its direct relationship with temperature.The values are especially low over the deserts and high in equatorial and monsoon regions.

 

 

Figure 8: World Distribution of Precipitable Water Vapour

Source:https://photojournal.jpl.nasa.gov/jpeg/PIA12097.jpg

 

The distribution of absolute humidity is extremely variable. It is maximum in the equatorial zone throughout the year and it is lowest in subtropical high pressure areas of Central Asia in winter and over the Antarctic. It decreases from equator towards poles. It also decreases from oceans to continental interiors.

 

Specific humidity decreases from equator to poles (Figure 9). It is extremely low (about 0.2 g/kg) in cold and dry regions over arctic region in winter season and it is highest in equatorial region (about 18 g/kg). On global scale, the range of specific humidity varies from 100 to 200 times for largest values as compared to the least. It is considered as a geographer’s yardstick of basic natural resource – water. Specific humidity is temperature controlled. Therefore, it is higher in summers than in winters (Figure 10 and 11). It is also higher over the oceans as compared to landmasses.

 

Figure 9: Distribution of Specific Humidity

Source:http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/media/graphics/spec_humidity_ssmi_amsu.gif

Figure 10: Seasonal Variations of Specific Humidity

Source: http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/media/graphics/jan_jul_spec_humidity.jpg

 

Figure 11: Distribution of Specific Humidity

Source: Khullar, D.R (2012), P-588.

 

The vapour pressure distribution is similar to specific humidity pattern (Figure 12).

 

Figure 12: Distribution of Vapour Pressure and Relative Humidity

 

Source: Critchfield, H.J. (1983), P-45.

 

It is noteworthy that the distribution pattern of relative humidity is different from specific humidity and vapour pressure. It is highest in equatorial zone and minimums in sub-tropical high pressure belts (Figure 12). From sub-tropical belts poleward it again increases towards the westerlies wind belts. Another significant feature of the distribution of relative humidity is shifting of the belts of highest and lowest relative humidity with changes in overhead position of sun. Relative humidity also generally decreases from oceans to continental interiors (Figure 13)

 

Figure 13: World Distribution of Relative Humidity

Source: https://i.stack.imgur.com/y5xki.jpg

 

There are latitudinal variations in the seasonal distribution of relative humidity. In the tropical regions the mean relative humidity remains higher in summer than in winter. Here, generally summers are wet and winter dry. In contrast, the high latitudes record the maximum relative humidity during humid winters. Remember that relative humidity on landmasses is dominantly controlled by temperature. Therefore, on the landmasses maximum relative humidity is recorded in winters as compared to summers. The exception to this generalization is monsoon region, where relative humidity is higher in wetter summer as compared with drier winter.

 

The diurnal variation in relative humidity is also well recorded. It is maximum in the early morning hours and minimum during the mid-afternoon time. This is due to indirect relationship with temperature (Figure 14).

 

Figure 14: Diurnal Variation in Relative Humidity

Source:http://environdata.com.au/wp-content/uploads/2016/07/Relative-Humidity-with-Temp.jpg

 

Instrumental Measurement of Humidity

 

A lot of instruments have been devised to measure humidity directly or indirectly. The most common instrument for measuring relative humidity is a ‘wet-and dry-bulb thermometer’. As the name indicates, in this, two thermometers are used and bulb of one is kept wet. When air is saturated, both the thermometers show the same values. Otherwise evaporation changes values in wet thermometer. The difference in values is used to obtain the relative humidity from the tables available (Table 2). For instance, if the dry-bulb thermometer reads 220C and the wet-bulb 160C, the relative humidity as seen in the table is 53 per cent.

 

Table 2 Measurement of Relative Humidity

Source:http://climisatolologyseattleandkodiak.weebly.com/uploads/2/6/2/7/26272361/5192064.jpg?466

 

For maximum evaporation, whirling psychrometers (thermometers in a sling or a kind of rattle) and the with small electric fans, the assman psychrometer have been devised (Figure 15 and Figure 16)

 

Figure 15: Whirling Psychrometer

Source:https://4.imimg.com/data4/JJ/JJ/GLADMIN-/images-whriling_hygrometer_preview-500×500.jpg

 

Figure 16: Assman Psychrometer

Source:https://img.tradeindia.com/fp/1/001/849/assman-psychrometer-180.jpg

 

For continuous records of relative humidity, hygrograph is used. This uses stands of human hair, which lengthen and shorten as per humidity levels. These minute changes are amplified and marked in ink by pen on a chart fixed to a rotating drum (Figure 17). The hair hygrometer also operates on the same principle. But the accuracy level of hair hygrometer is much less than instruments like the psychrometer. Aninstrument known as the infrared hygrometer uses a beam of light projected through the air to a photoelectric detector to measure humidity. Still another device called dew point hygrometer use artificially cooled surfaces to determine the dew point temperature directly.

 

Figure 17: Hygrograph

Source: https://en.wikipedia.org/wiki/File:Umidaderelativa.jpg

   Summary and Conclusions

 

Humidity denotes the amount of water vapour present in air. The content of humidity in air varies from place to place and fromtime to time. It ranges from almost zero in the cold and dry air of arctic regions in winter to about 5 per cent in the hot and humid equatorial region.In determining the weather and climatic conditions its state changes and associated transformation of heat play a vital role. The hydrological cycle represents interchanges of physical states as well as geographical positions at global scale.The well known measurements of humidity are following – (i) absolute humidity; (ii) specific humidity; (iii) mixing ratio; (iv) vapour pressure and saturation;(iv) relative humidity and (v) dew point temperature.Absolute humidity is the mass of water vapour in a given volume of air. It is generally expressed as grams per cubic meter of air.The actual amount of moisture present in air is expressed by specific humidity. It is the ratio of mass of the water vapour to the mass of air, including water vapour. It is usually expressed as grams per kilogram of air. It is not affected by changes in pressure and temperature. Mixing Ratiois closely related to specific humidity. It is ratio of the mass of water vapour in a unit air compared to the remaining mass of dry air.It is measured in the units of mass, usually grams per kilogram, like specific humidity.

 

The vapour pressure measure of the moisture content of the air is derived from the pressure exerted by water vapour. It represents the partial pressure exerted by water vapour in the air. It is measured in the same units used for barometric pressure i.e. millibars.The saturation situation pressure is called saturated vapour pressure.The temperature of air at this time represents its dew point temperature, or frost point (if below freezing). The saturation vapour pressure is temperature-dependent. At higher temperatures more water vapour is required for saturation. It is noteworthy that for every 100C increase in temperature, the amount of water vapour needed for saturation almost doubles. The difference between the water vapour holding capacity and actual amount of moisture present in air is known as the saturation deficit.

 

Relative humidity is defined as the ratio of the actual water vapour content in the air to the amount of water vapour required for saturation at that particular temperature in the same air. Therefore, it does not represent the actual amount of water vapour in air but shows only how far or how near the air is from saturation.It has no unit of measurement and is always expressed in percentages. Relative humidity can also be expressed as the ratio of the observed vapour pressure to that required for saturation at a particular temperature.

 

Dew-point temperature or simply dew point is another significant measure of humidity. It represents the temperature to which air is cooled to achieve saturation. It is easy to determine because of its direct association to the amount of water vapour in the air. Dew-point temperature has emerged as one of the most significant measures of humidity. It is used to determine association of the amount of moisture with human comfort.

 

There are spatial and temporal variations in the distribution of humidity. These variations are common in vertical distribution as well as horizontal distribution. About half of the atmospheric moisture is concentrated below about 1450 meter and more than 90 per cent of the water vapour is below 5,575 meter. The seasonal variations in vertical distribution of humidity are mainly up to the height of 3,000 meter or so. It is noteworthy that the vertical concentration of humidity decreases form equator to poles.

 

The distribution of absolute humidity is extremely variable. It is maximum in the equatorial zone throughout the year and it is lowest in subtropical high pressure areas of Central Asia in winter and over the Antarctic. It decreases from equator towards poles. It also decreases from oceans to continental interiors.

 

Specific humidity decreases from equator to poles. It is extremely low (about 0.2 g/kg) in cold and dry regions over arctic region in winter season and it is highest in equatorial region (about 18 g/kg).It is considered as a geographer’s yardstick of basic natural resource – water.

 

It is noteworthy that the distribution pattern of relative humidity is different from specific humidity and vapour pressure. It is the highest in equatorial zone and minimums in sub-tropical high pressure belts.From sub-tropical belts poleward it again increases towards the westerlies wind belts. Another significant feature of the distribution of relative humidity is shifting of the belts of highest and lowest relative humidity with changes in overhead position of sun. Relative humidity also generally decreases from oceans to continental interiors.

    There are latitudinal variations in the seasonal distribution of relative humidity. In the tropical regions the mean relative humidity remains higher in summer than in winter. Here, generally summers are wet and winter dry. In contrast, the high latitudes record the maximum relative humidity during humid winters. The diurnal variation in relative humidity is also well recorded. It is maximum in the early morning hours and minimum during the mid-afternoon time. This is due to indirect relationship with temperature.

 

A lot of instruments have been devised to measure humidity directly or indirectly. The most common instrument for measuring relative humidity is a ‘wet-and dry-bulb thermometer’. The others are whirling pshychrometer and assman psychometer which are its advanced forms. Hygrometers of various types and hygrograph are also commonly used devises to measure and record humidity.

 

you can view video on Atmospheric Moisture Humidity – Measurement and Distribution

 

References

  • Barry, R.G. and Chorley, R.J. (1998) Atmosphere, Weather and Climate, Routledge, London.
  • Critchfield, H.J. (1983) General Climatology, PHI Learning Private Limited, New Delhi. Frederick,
  • K.L and Edward, J.T. (2010) The Atmosphere – An Introduction to Meteorology, PHI Learning Private Limited, New Delhi.
  • Husain, M. (2002) Fundamentals of Physical Geography, Rawat Publications, Jaipur.
  • Lal, D.S. (1993) Climatology, Chaitanya Publishing House, Allahabad.
  • Lal, D.S. (2009) Physical Geography, Sharda PustakBhawan, Allahabad.
  • Oliver, J.E and Hidore, J.J. (2003) Climatology: An Atmospheric Science, Pearson Education, Delhi
  • Singh, S. (2015) Physical Geography, Pravalika Publications, Allahabad.
  • Strahler, A.N. and Strahler, A.N. (2001) Modern Physical Geography, John Wiley and Sons, Singapore.
  • Trewartha, G.T. and Horne, L.H.(1968) An Introduction to Climate, McGraw-Hill, New York.

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