Spatial and temporal variability

Rainfall is the key driver of flow generation processes, however it is highly variable in both space and time. The effect of spatial variability on streamflow hydrograph generation has been widely investigated over many years resulting in varying conclusions which have yet to be resolved (Emmanuel et al., 2015). Every catchment and every rainfall event is different which, when coupled with errors, that may be large enough to obscure any patterns, lead to a complexity which make it difficult to draw any general conclusions (Emmanuel et al., 2015; Segond et al., 2007). Timescale and sampling interval may also have an impact.

Rainfall variability in both space and time over the 135 km2 _{Brue catchment in South-} west England is illustrated in Figure 2-1below. The Brue catchment is unusual due to density of the rain-gauge network. It has 49 rain-gauges in a catchment of 135 km2. Many of the gauges are very close together and therefore highly correlated (see Figure 7-3 in chapter 7). The 23 gauges used in this study, a density of 1 gauge per 5.9 km2, maintain geographical coverage. In practice, it is likely that a catchment of this size would only have a network of 2 or maybe 3 gauges (in 2010, the UK average was one gauge per 76 km2,Met. Office, 2010). The density of the gauge network makes it ideal for investigating the effect of spatial rainfall distribution on flow generation. It was set up as part of the Hydrological Radar Experiment (HYREX) by the UK Natural Environment Research Council (NERC) that ran from May 1993 to April 1997. The broad aim of HYREX was to gain a better understanding of rainfall variability, as sensed by weather radar, and how this variability impacts on river flow at the catchment scale (Moore et al., 2000). For further discussion, see chapter 3, section 3.3.

C hapt er 2 Ba ck gr ound to m ethods 18 Figure 2-1: Maps of rainfall over the Brue catchment showing the variability in time and space. The brighter the color, the higher the rainfall. The pie chart at top right shows the proportion of gauges measuring rain in the illustrated time step (more yellow - more gauges with rain).

Time step 8, max. 0.4 mm, mean 0.06 mm Time step 164, max. 3.2 mm, mean 0.55 mm

Time step 2540, max 5.2, mm, mean 2.42 mm

mmn 2.42 mm

19 Beven and Hornberger (1982) suggested, on the basis of a simulation study, that spatial variability is important, leading to significant differences in peak timing, distributions of peak flow and affecting volume - getting the volume right seems to be most important. The effects of spatial variation are tied to the question of how many gauges are needed to achieve an accurate estimate of catchment rainfall (Adhikary et al., 2015). Dense gauge networks which might be expected to give a better estimate are expensive to install and maintain but sparse networks may miss the detail of rainfall variation especially under convective conditions. There is an example of two gauges only 300m apart in Walnut Gulch, Arizona showing a difference of 10mm from one convective storm (Faurès et al., 1995). A large body of research exists aimed at answering the question of rain gauge location and network density. A very brief overview is given here. For further details, refer to the referenced literature.

The variability of rainfall is damped by the catchment processes so streamflow shows less variability. If rainfall variability is not organised enough to overcome the damping effect, then spatial variation need not be taken into account however reliable information on spatial patterns is important in order to make accurate estimates of total volume. This may be more important than spatial variation in itself (Obled et al., 1994; Segond et al., 2007). The importance of spatial variation may be catchment specific and dependent on the characteristics of the catchment and the rainfall regime. Younger et al., (2009) studied the effect of rainfall input on model output on an event-by-event basis in the Brue catchment. They concluded that errors in the rainfall can lead to changes in the estimated model parameters to compensate for these observation errors. This may lead to a set of parameters for a single average model that is uniquely adjusted to simulate the erroneously observed event or events.

A well-designed network is required to evaluate an accurate estimate of the rainfall (Adhikary et al., 2015), one that is dense enough to give a good estimate with gauges in the right locations but without redundancy. One of the earliest studies of the effect of network density was carried out by Eagleson (1967) using a combination of harmonic analysis and distributed linear systems (having some similarity to the techniques used in this study). He claimed that incorporating catchment dynamics into network design reduces the number of gauges required. Bras and Rodriguez-Iturbe (1976) used a multi- variate state-space rainfall model together with a runoff model to investigate how

Chapter 2 Background to methods

20 detailed the description of the rainfall field needed to be. Both Eagleson and Bras and Rodriguez-Iturbe concluded that gauge location appeared to be important and that catchments are more sensitive to storms dominated by over-land flow near their outlets. The HYREX experiment (Moore et al., 2000) was set up to investigate rainfall variability and its impact on catchment scale flow regimes by combining radar and remote sensing data with information derived from a dense rain gauge network over the Brue catchment. Zhang and Han (2017) investigated spatial variability using the same catchment as a case study. They presented a framework for assessing spatial variation based on a combination of Coefficient of Variation and Moran’s I (Moran, 1950) and concluded that a simple lumped model was adequate for simulating simple events but models with higher spatial resolution were required for more complex spatially variable events.

Lebel et al., (1987) used scaled estimation error variance to compare Thiessen polygon, spline and Kriging interpolation methods for a range of network densities. Lebel et al., (1987), Obled et al., (1994) and Shah et al (1996) all stated that a dense network has advantages over sparse networks whilst Sugawara (1992) said that rain gauge weighting should be by meteorological conditions rather than location. Several other studies looked at the impact of the density of gauge networks on rainfall estimation and hydrograph generation (c.f. for example, Anctil et al., 2006; Bardossy and Das, 2008). The introduction of weather radar and other remote sensing techniques has led to several studies aimed at reducing uncertainties in rainfall forecasts by combining radar and remote sensing data with information derived from rain gauges (c.f. for example, Moore et al., 2000; Bradley et al., 2002; Brocca et al., 2013). Chandler and Wheater (2002) applied Generalised Linear Models (GLM) to a cluster of flood events in western Ireland and suggested that GLMs could be a powerful tool for analyzing historical records for rainfall variability patterns potentially associated with climate change. With advances in Geographical Information Systems (GIS), greater use is being made of geostatistical techniques both to investigate the effects of rainfall variability and to improve rainfall estimates (c.f. for example, Naoum and Tsanis, 2004; Yeh et al., 2011; Shaghagian and Abedini, 2013; Adhikary et al., 2015) however these techniques require that a large number of gauges are available for analysis.

21 It is often the case that a single gauge or sparse gauge network is assumed to represent the catchment as a whole. In this study, a method for assessing which gauges are representative using DBM modelling is proposed (see Chapter 7). It can be shown that representativeness varies with time due to the movement of rainfall over the catchment. The method highlights that spatial rainfall distribution does indeed have an impact on runoff (surface and sub-surface) generation. It is proposed, in Chapter 7, that reverse hydrology can be used to overcome this problem.