# Flow Sensitivity

How sensitive are river flows to variations in precipitation and temperature?

A question is, how sensitive is runoff to variations in precipitation and temperature? This is important not only historically, but to establish a region-specific basis for evaluating potential response to climate changes. One way of examining this problem is to take the historical records of precipitation, temperature, and runoff, and "perturb" them by specific amounts, to determine what is called sensitvity and elasticity.

Both daily temperature and precipitation for the Wood and Lettenmaier dataset were perturbed by the same amount throughout the record period (1970 – 2006). With the actual gridded precipitation data as a baseline, additional reference climates were created as 70%, 80%, 90%, 110% and 120% of the current precipitation. Thus, there were 6 different forcings from the precipitation perturbation only. Similarly, the actual gridded temperature (both tmax and tmin) were used as a reference, with additional climates created by adding 1, 2 and 3 ºC to daily minimum and maximum temperatures.

An aridity index, defined as the ratio of potential ET to precipitation (Budyko, 1974), is often used to estimate annual runoff change as a result of climate change at larger scales (Arora, 2002). However, since ET is influenced by a number of climatic variables, the aridity index does not explicitly inform as to how much a change in P and T affects a basin’s runoff. In this study, a formulation used by Vano et al. (2012) was used to compute precipitation elasticity and temperature sensitivity. The precipitation elasticity, ε, is computed as the change in mean annual runoff  (Q), divided by the change in precipitation (P), with the change P set to be 1%,

where Qref is the mean annual runoff for a given grid cell corresponding to a reference P. For instance, for P at 110% of the historical P value, Qref is runoff for 1.1P. Thus, Qref+∆ is runoff corresponding to 1.11P. The runoff sensitivity, S, to temperature change is computed same way as ε. However the temperature change, ∆, is not in % rather in absolute value equaling 0.1ᵒC.

For the S computation, we used the formulation as defined by Dooge. (2001) as the percent change in mean annual Q per 1ºC temperature change,

where ∆ is 0.1 ºC. The change is applied to both minimum and maximum temperatures.

To evaluate the combined effect of both temperature and precipitation change, both T and P were perturbed simultaneously by 1ºC and 1%, respectively. The resulting runoff is Q∆T∆P.  This runoff was then compared to the runoff computed using Equation 3, as outlined in Vano et al. (2012).

where QH is historical runoff with current T and P unchanged, Q∆T is runoff with T +1oC and P unchanged, Q∆P is runoff with 1.01P and T unchanged.

The precipitation elasticity values,  were calculated both spatially and at individual station points.  The values ranged from 1.5 to 12 and for all gauges, decreased with increased precipitation. For example, if  is 3, a 10% decrease in precipitation would result in a 30% decrease in streamflow. Likewise, for the same , a 10% increase in precipitation would result in a 30% increase in streamflow.  The elasticities show that a decrease in precipitation is will more significantly affect streamflow than an increase in precipitation since runoff and baseflow are limited both by soil saturation and evaporation. Elasticity values greater than one, and strong increases in elasticity with declining precipitation, denote water limitations. These limitations become increasingly severe as precipitation declines. This is consistent with the Budyko hypothesis and analysis of climate sensitivities by Dooge (1992).

For temperature sensitivity, S remains relatively unchanged relative to the reference T for all the gauges. Sensitivity increases slightly after a 3°C perturbation (Figure 3). The magnitude and direction of S demonstrates how land-surface hydrology can both exacerbate, and more rarely modulate, regional scale sensitivities to global climate change. Generally, as T increases, ET increases and runoff decreases (resulting in negative S).