Water Supply

A thorough analysis of river flow would require analytical calculus, statistics and other very tedious college level mathematics. But to understand floods and droughts only takes a bit of intuitive thinking which we might call "conceptual calculus." Here we will look at the conceptual calculus of water flow. We will show how this conceptual calculus will lead us to recognize variations on floods and droughts that are easy to overlook. From that we can promote awareness of variables relating to water supply. Here we will show how droughts and floods have multiple forms and cannot be understood using average rainfall, river level or other common methods. Still floods and droughts can be understood without using advanced analytical methods.

Climate regions are commonly defined by their average annual rainfall. Averages are easy to misinterpret. An area can have an average annual rainfall of 23 inches. But if it gets 23 inches of rainfall one day, then no rain the rest of the year, the area will have a few days of flooding followed by eleven months of drought. A variation of this actually happened in the Atlanta GA area a few years ago. Atlanta had a record drought. The drought ended with a record rain event which flooded many parts of the city. So, at the end of the year the record showed that Atlanta had nearly normal annual rainfall.

Draft: September 2011




  1. droughts
  2. floods
  3. summation
  4. analysis



The conceptual calculus of drought is rather straight forward. Drought occurs when the rate of outward flow over time (the integral of outflow) remains larger than the rate of flow in over the same time (the integral of inflow.) But we must recognize that we use water in four different places or sources. Thus, four types of droughts must be understood. The environmental implications of drought are actually more difficult to understand. Drought occurs when there is insufficient water to sustain various ecosystem functions or human activities. But we must understand biology, environmental science or chemistry to determine what systems are not being maintained. Thus, a simple numerical definition of drought might not sufficiently match the environmental implications of a drought.
By thinking about where our water comes from we recognize four types of droughts. Each type of drought results from different factors. One type of drought may persist even while the others end.

1. River Drought: The calculus: River droughts occur when the rate at which rain, snow melt, and ground water seepage remain lower than the rate the water flows away in the river for extended periods of time. The environment: The low flow rate becomes a drought in environmental terms when insufficient water remains in the river for the river to support its normal aquatic life level or riparian ecosystems. This may result from insufficient water to maintain oxygen levels or dilute impurity levels.
2. Reservoir Drought: The Calculus: A reservoir drought occurs when water gets removed from the reservoir faster than river flow can replenish it. Water usage increases with agriculture, industry, population, leaks, and low efficiency (all these factors are part of the integral.) Replenishing waters come primarily from weather and climate factors.
3. Field drought: The calculus: Field droughts occur when the soil fails to maintain enough moisture to support crops. Water is drawn out of the soil primarily by evaporation, roots, and seepage into deeper aquifers. Tilling soil and reducing plant diversity can increase losses to evaporation. So can wind and low humidity. Water is absorbed primarily from rains and snows. However, the absorption has a highly nonlinear relationship with precipitation rate. Most of the water from a heavy rain rapidly runs off the top of the soil into the river. A field drought can start shortly after a heavy rain even while the reservoir is full. Much of the moisture from slowly melting snow tends to soak into the soil. Thus a cold wet winter tends to be good for field water. The soil absorption rate can be slowed by compression from traffic, impermeable membranes such as roads, patios, and lawns, and water drainage projects. Thus, traffic and construction can contribute to field droughts.
4. Well water drought: The calculus: Water seeps slowly from the surface through fissures in rocks into wells. Ground water droughts occur when water is drawn out of wells over an extended period of time quicker than ground percolation replenishes it. Draw increases with population and usage. Replenishing flow is limited by natural rock percolation speeds and flow through the surface. Flow through the surface can be seriously reduced by construction, compression, and water diversion.

Floods & Excess Water
Like drought, there is more than one type of excess water. Ecosystems need the correct amount of water. More is not better. Within the normal range is best. We are all aware of floods, but we must remember floods are not the only excess water problem.

1. Floods: When we think of excess water, we think of rivers overflowing their banks - floods. We must remember that periodic flooding is normal and many ecosystems and species depend on periodic flooding. The traditional view of a flood is the river overflowing its banks. But this overflowing is not a problem, and may actually be good for the environment, unless the overflow impacts man-made structures, human activities, or washes contaminants from the land into the river. From this we realize that there are two levels of flooding to be aware of. (1) A river may overflow its normal banks and spread across the flood plain. When humans are not impacted, flooding is typically a healthy part of a natural cycle. (2) A flood may damage man-made structures, or wash tilled soil off of farms, or wash contaminants off land into the river. A flood becomes a problem, not when rivers overflow their banks, but when human activity encroaches on the flood plain.
2. Persistent rain: Many plants and most crops need a critical amount of time to dry out after rain. If they don't dry out they start to mold and rot. For some plants even light rainfall occurring persistently will destroy the fruit. Thus excess water conditions may occur even without flooding.

Twice in the last fifteen years the area where the author lived had summers with excess rain. The rivers did not flood during these spells. So no reports of record rain occurred. But tomatoes and other fruits rotted on the vines. This contrasts to our example above. An average of 23 inches of rainfall a year would equal about 1/16 of rain each day. But persistent rain will contribute of fungus and mold which will rot most of the crops and fruits.

It is easy to understand the extremes of floods and droughts. But recognizing the onset of droughts or excess water actually proves to be quite tricky. The ideal scenario requires water to be supplied at a somewhat regular rate, and dry weather to come at a regular rate also. This cannot be measured by averages. Deviations from ideal cannot be fully understood by counting outliers (floods and droughts.) Yet, measuring averages and counting outliers are the two methods we are most familiar with.
Floods are short term. Floods make for easy video footage for the news. Thus we recognize floods readily. Droughts are long term. It will take time for the available water to flow away. Light rain usually occurs during this time. Thus it is somewhat tricky to recognize a drought until it is too late to make adjustments. Similarly, persistent rain does not become a problem until the fruits and crops start to rot. We don't see it coming. We can't take impressive videos of the power of its impact. But it will affect us.

It is not safe to conclude that normal annual rainfall means that no drought exists. Field moisture and ground water may still be low. It is not safe to conclude that a heavy rain will end drought conditions. Field moisture and ground water cannot be directly determined from the total rain amount or river level as heavy rains run off the fields into the rivers. Long term averages and outliers don't really tell us whether we have healthy water conditions to maintain ourselves. Although the simple methods we want to use don't give us the information we want, we can still develop methods to review data. We can still make plans by comparing our needs and usage to past patterns of water flow.

Another website looked at average rainfall across North America. They found that over the last 50 years just a slight increase in average annual rainfall occurred. From this they concluded that climate change was not having a significant affect on our rainfall. But as we discussed above total annual rainfall doesn't really tell us very much. What we need to know is how much the rainfall deviates from the optimal rates that will replenish our reservoirs, soil moisture, and groundwater, and still give our crops and houses sufficient time to dry out. The reservoir, groundwater, and soil water do not all have the same optimum conditions.


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Analysis of Bee Tree Creek


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