Abstract
Recent work has identified potential multi-year predictability in soil moisture (Chikamoto et al. in Clim Dyn 45(7–8):2213–2235, 2015). Whether this long-term predictability translates into an extended predictability of runoff still remains an open question. To address this question we develop a physically-based zero-dimensional stochastical dynamical model. The model extends previous work of Dolgonosov and Korchagin (Water Resour 34(6):624–634, 2007) by including a runoff-generating soil moisture threshold. We consider several assumptions on the input rainfall noise. We analyze the applicability of analytical solutions for the stationary probability density functions (pdfs) and for waiting times for runoff under different assumptions. Our results suggest that knowing soil moisture provides important information on the waiting time for runoff. In addition, we fit the simple model to daily NCEP1 reanalysis output on a near-global scale, and analyze fitted model performance. Over many tropical regions, the model reproduces the simulated runoff in NCEP1 reasonably well. More detailed analysis over a single gridpoint illustrates that the model, despite its simplicity, is able to capture some key features of the runoff time series and pdfs of a more complex model. Our model exhibits runoff predictability of up to two months in advance. Our results suggest that there is an optimal predictability “window” in the transition zone between runoff-generating and dry conditions. Our model can serve as a “null hypothesis” model reference against more complex models for runoff predictability.
Highlights
There are several approaches to modelling and predicting water runoff (Nash and Sutcliffe 1970)
In the NCEP1 reanalysis soil moisture model, infiltration rate is equal to the precipitation up to the so-called maximum infiltration rate, and any excesses which can not evaporate turn into runoff (Mahrt and Pan 1984)
We develop a physically-based stochastic–dynamical low order model of soil moisture and runoff motivated by the previous work of Dolgonosov and Korchagin (2007)
Summary
There are several approaches to modelling and predicting water runoff (Nash and Sutcliffe 1970). They combine computational simplicity with a physically-based framework (Naidenov and Sveikina 2002; Dolgonosov and Korchagin 2007; Bartlett et al 2015; Zielinski 1984) Despite advances in this area, such models have not been sufficiently tested against more complex climate models which represent both atmospheric dynamics and land surface processes. Some studies (Naidenov and Sveikina 2002; Dolgonosov and Korchagin 2007) do not consider a hydrologic threshold—a value of the system state at which the system exhibits sudden changes in dynamics (James and Roulet 2009; Penna et al 2011; McMillan et al 2014, and others) An example of such a threshold is runoff that abruptly increases above a certain soil moisture value. We adopt the stochastic dynamical modeling approach since our goal is to analyze runoff predictability and to directly relate runoff pdfs and return waiting times to the properties of the hydrologic system. We conclude our analysis by comparing the model to NCEP1 reanalysis output (Sect. 4) and to the original model of DK2007, discuss some model caveats (Sect. 5) and provide a future outlook (Sect. 6)
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