Water Balance Model for Environmental Sustainability Analysis

This project analyzes the principles of environmental sustainability through a water balance model, focusing on precipitation rates, runoff, and residence times. The assignment involves calculating key water balance expressions and constructing an Excel model to explore the implications of future climate changes on the hydrological cycle. The student describes the water cycle processes, including precipitation, evapotranspiration, and runoff, and defines concepts like the water footprint. The project also includes calculations for average residence times of water molecules in the atmosphere and the runoff ratio, crucial for understanding water resource management and potential flood control measures. The detailed analysis provides insights into the relationships between different components of the water budget and their significance in a changing climate. The student addresses the water balance equation, its components, and the factors affecting the hydrological cycle, providing a comprehensive overview of the topic.

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Student’s Name
Professor’s Name
Course
Date
Principles of Environmental Sustainability
Rate of precipitation to the land
Precipitation is denoted by the water directly released from the sky as rain, snow and hail.
Because of its nature, it is the main linkage in the water cycle which provides for the delivery of
sky water to the earth surface. However, most precipitation falls to the land surface as rain. The
higher levels of the sky is always cooler compared to the earth surface hence condensing the
water vapor water droplets that later falls back to the land surface as precipitation. Thus, the tiny
(invisible) water vapor will condense into tiny water droplets in the form of clouds. To
determine the rate of precipitation, it is important to determine the amount of runoff to the land
and the sea. This procedure is done by adding the rate of precipitation to the land PL (ESL) and the
evaporation rate from the land which is received back to the land as rain (ELL)
Therefore PL=R=ELL+ELS=46×103 km3/yr.
Rate of precipitation to the sea
Several water cycle studies takes keen note of the processes and changes which takes place
within the land surface water with little done on the behavior of the ocean runoff. Usually, the
ocean covers about 75% of the earth’s surface and thus a channel for most of the precipitation
and evaporation of the surface water. Most of the global precipitations are formed from the
storms which develop within the intertropical convergence zones. These storms normally
converge within the south and north of the equator due to the excessive heating over these

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regions hence causing rainfall over the regions. Therefore, rate of precipitation over the sea is
represented evaporation rate from the land that falls as precipitation on the sea (ELS) and
evaporation from the sea that falls as the precipitation on the surface of the land ESL.
To clearly define the problem, box model identification is necessary to state the boxes
and the fluxes between them. The surface runoff is link to the sea and land boxes. It is therefore
assumed that some percentage of the evaporation falls back as precipitation over the sea leading
to hydrological cycle balance. The problems provided can be restated in form of the behaviors
of the runoff (R), precipitation (P1), the change in evaporation onto land (ELL) and
evapotranspiration onto the sea (ELS). By using the water balance approach, three water
conservation approaches exist. First, sum of the precipitation within the sea and surface run of
rate (equivalent to the rate of evaporation from the sea). Secondly, denotes the precipitation
within the land and the amount of evaporation from the land surface. The third factor takes into
consideration the sum of land runoff and evapotranspiration from the land surface to the sea
which is equivalent to the rate of evapotranspiration from the sea to the land surface. By
combining two and three, the rate of precipitation on the land (P1) in relation to the land
evapotranspiration (ELL) and the evaporation rate from the sea to the land denoted as ESL.
Combining one and two helps to express the value of the sea precipitation (Ps) to the value of the
land evapotranspiration to the sea (ELS) and the rate of evapotranspiration from the sea to the sea
hence determine the total value of the influx.
b). Calculating the average residence times for a molecule of water in the atmosphere
The residence time represent the average length of time a molecule of water takes to remain in
the water reservoir. The measurement is only used for water reservoir that is at a steady state. In
other words, residence time is takes into consideration the mass of the material in the reservoir

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divided by the value of the outflow and the inflows preferably when the reservoir is at
equilibrium. Moreover, where there is several inflow and outflow, the residence time is
determined by the value of the sum of both outflows and inflows to and out of the reservoir. The
residence time is determined by the formula below.
Residence time= Amount of water ∈the reservoir
outflow ( ¿ inflow ) at steady state = 37.5× 106 km3+1350 × 106 km3
0.013× 106 km3 =284 days
C). the ran off ratio
The ratio the amount of water that infiltrate into the soil and therefore important in controlling
the floods. It can assist to determine the height of dams constructed to control floods in a
particular area.