Hydroclimatology is the study of the relationship between climate and the water on earth. Thus, the water or hydrologic cycle is the central issue in hydroclimatology. Using conservation of mass, the following water budget equation has been derived:
P = R + ET + U + SS + SG + I
P is precipitation; R is streamflow (surface runoff); ET is evapotranspiration; U is subsurface underflow; SS is the change in soil moisture; SG is the change in groundwater storage; and I is interception.
Precipitation is the amount of water that falls and is usually measured by catching rain and snow in a canister and measuring the depth. Surface runoff can be divided into three parts: immediate runoff following precipitation, lagged runoff from snow and ice melting, and runoff for interflow if reentering into a stream. Each of these runoffs happen in a delayed fashion following precipitation. The lag time for each of these parts vary greatly.
Evapotranspiration is the moisture loss that moves from the soil to the air, or from vegetation to air. It depends on the energy source (i.e. Sunlight on the soil and vegetation), the vapour pressure and the windspeed. Subsurface underflow and groundwater storage change are very difficult to distinguish when measuring so they are often measured as one. Changes in soil moisture refers to the water that soil will absorb from surface water. It is measured by removing a column of soil and measuring the moisture before and after it is heated; then, you can subtract the dried soil weight from the calculation.
Lastly, interception is the precipitation that lands on the surfaces of vegetation, buildings, and soil surfaces. It is often assumed to be quite minimal. Often times you will see this same equation written simply as:
P = R + ET
This is because when annual mean data is analyzed, it is found that subsurface underflow, changes in soil moisture, and changes in groundwater storage are almost zero. Furthermore interception is usually sufficiently small. So, those four terms are removed leaving a much simpler equation to deal with.
Title Image Credit: Geograph. (2014). Leithen Water flows into the River Tweed. Retrieved from http://www.geograph.org.uk/photo/1286882