Variability is the change in hydrological quantity when comparing one spatial location with another, or one time with another. Variability occurs naturally, and also because of human activity (e.g. land cultivation, urbanization, and forest management). We can see evidence of this variability in measurements of rainfall, air temperature, soil moisture, snow cover, groundwater level, and streamflow, or any other hydrological quantity. Everyday life already provides us with an intuitive understanding of the many aspects of variability, for example, from the common experience that air temperature is variable with space and time.
We know about the time variation of temperature on at least three different scales: first, it is generally cooler at night and warmer during the day; second, daytime temperatures are cooler on cloudy days; and third, it is generally cooler in winter and warmer in summer. These three examples of temporal variability are at different timescales: the first is at the daily timescale, the second has no particular timescale (cloudiness may last for seconds or for days), and the third is at the annual timescale (we will define the concept of scale more carefully in the following text). We also know that air temperature is variable from place to place: it is cooler in the shade of a leafy tree than standing out in the sun, and it is cooler on the mountaintops than in nearby lowlands.
We thus have experience of spatial variability for at least two space scales, the plant scale (of the order 1 m) and the landscape scale (perhaps 10 km). Scale in this article is used to mean a spatial or temporal measure over which a hydrologic variable is being considered. For example, we may think of the amount of water held in the rooting zone of a soil at an instantaneous timescale, or an average value over the timescale of a day or a year or other period. When we choose a scale, this affects how we perceive soil moisture, or whatever other phenomena we care to think of. If we look at the moment-to-moment variability of instantaneously measured soil moisture, we see a particular variation.
If we examine daily averaged soil moisture at the same place over the same period, we see something different. This difference is the effect of timescale on variability Similarly, we can consider this soil water at the spatial scale of a “point” or a field average, or a catchment average. Again, a change in the scale of observation causes a change in the perceived variability.
Hydrological Variability at a Range of Scales.
Hydrological variability makes the hydrologist’s task both interesting and challenging. The same phenomenon has to be treated differently depending on the space and timescales of the problem being considered. At the simplest level, hydrologists treat variability by measuring or estimating the variations at scales that are relevant to the problem at hand (and can be measured), neglecting other variations. This distinction is also referred to as resolved and unresolved variability. The selection of appropriate time and space scales at which to resolve variability is often a challenging task.
¨ The spatial or temporal scale we use has a great effect on the variability we perceive: the scale can act as a filter, which lets us see some aspects of hydrology and masks out others. We can of course make very detailed observations over long time periods or over large regions, encompassing many sources of variability (e.g. hourly rainfall measurements for many years, or satellite imagery at 5 m resolution over thousands of square kilometers). However, humans do not generally comprehend all these scales at once, and typically take steps to reduce or compress the amount of information, perhaps by reducing resolution (e.g. using time series of monthly rainfall), or by reducing the extent of the data set (e.g. using only a day of 15-s rainfall data).
The Nature of Variability: Random and
Deterministic .
Descriptions of variability can be divided into two main types: random (happening by chance, unexplained, stochastic, probabilistic) and deterministic (caused by preceding events or natural laws, predictable, cyclic, trend, pattern).One extreme worldview is that all hydrological variability is deterministic, because every hydrological event has a cause that is knowable at least in principle. However, there are many situations in which the deterministic approach is impractical. There is a long history of treating hydrological quantities as random phenomena, not because they are intrinsically unpredictable, but simply because the random approach is convenient for some tasks. There are also situations in which detailed knowledge of variations and their causes is less helpful than identifying an effective descriptor, such as a statistical parameter or distribution, which captures the essential behavior of the system, without requiring a detailed enumeration of every part of the system. A well-known analogy is the use of thermodynamics to describe the net effect of many interacting molecules, and indeed several attempts have been made to construct hydrological theories using this approach.
The same physical variable can be treated as a random quantity in one context, and as deterministic in another. As an example, consider the rain falling on a small area in a severe storm. For the purpose of understanding a catastrophic flooding event caused by a particular storm, it is appropriate to use detailed measurements of how much rain fell at what time and over which locations to understand the movement of storm runoff and the subsequent flooding. This is a deterministic approach to storm rainfall. However, when designing a structure to withstand severe storms, it is often more useful to consider storm occurrence to be a random phenomena and make a statistical description of storm rainfall, assessing the probability that an event of a certain magnitude might occur. Random and deterministic approaches can also be combined, so that, for example, one might consider the total depth of rain in a storm to be a random variable, but use one or more deterministic patterns to describe the expected temporal variation of rain intensity during any storm.
