Are simpler models less robust?
Authors: Santos Léonard , Royer-Gaspard Paul , de Lavenne Alban , Andréassian Vazken 
Published: March 2022

&lt;p&gt;Among the properties that a wise modeler would desire for his or her own model is the &lt;em&gt;capacity of extrapolation beyond known hydroclimatic conditions&lt;/em&gt;. Extrapolation capacity seems essential when a model is to be used to predict the impact of future conditions, which may not have occurred in the past (at least not during the calibration period). Hydrological good sense would let us imagine that the more complete the model, the better it should do in extrapolation. But because the wise should doubt even one&amp;#8217;s good sense, we wish to test this hypothesis, starting with a series of extremely simple models, working at the annual time step:&lt;/p&gt;&lt;ul&gt;&lt;li&gt;the simplest of all annual models is a linear one, using only annual precipitation&lt;em&gt; P&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; as explanatory variable: &lt;em&gt;Q&lt;sub&gt;n&lt;/sub&gt; = a.P&lt;sub&gt;n&lt;/sub&gt; +b&lt;/em&gt; (&lt;em&gt;Q&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; being streamflow for year &lt;em&gt;n&lt;/em&gt;, &lt;em&gt;a&lt;/em&gt; and &lt;em&gt;b&lt;/em&gt; being calibrated parameters);&lt;/li&gt;
&lt;li&gt;slightly more complex is a three-parameter linear model using both precipitation &lt;em&gt;P&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and potential evaporation &lt;em&gt;E&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; as input: &lt;em&gt;Q&lt;sub&gt;n&lt;/sub&gt; = a.P&lt;sub&gt;n&lt;/sub&gt; +bE&lt;sub&gt;n&lt;/sub&gt; + c;&lt;/em&gt;&lt;/li&gt;
&lt;li&gt;slightly more complex is a non-linear model based on the Turc-Mezentsev formula (Andr&amp;#233;assian &amp; Sari, 2019);&lt;/li&gt;
&lt;li&gt;again, more complex is a non-linear model based on the &lt;em&gt;Catchment Forgetting Curves&lt;/em&gt; (CFC) accounting for the pluriannual catchment memory (de Lavenne et al., in review);&lt;/li&gt;
&lt;li&gt;last, we use a much more complex daily time step hydrological model as reference.&lt;/li&gt;
&lt;/ul&gt;&lt;p&gt;To answer our title question, we test the robustness of these models of increasing complexity using a dataset of 555 French catchments, a specific metric (PMR - Royer-Gaspard et al., 2021) and the robustness assessment test (RAT - Nicolle et al., 2021).&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Andr&amp;#233;assian, V. and Sari, T.: Technical Note: On the puzzling similarity of two water balance formulas &amp;#8211; Turc-Mezentsev &lt;em&gt;vs&lt;/em&gt; Tixeront-Fu. &lt;em&gt;Hydrol. Earth Syst. Sci.&lt;/em&gt;, 23, 2339-2350, 2019.&lt;/p&gt;&lt;p&gt;de Lavenne, A., Andr&amp;#233;assian, V., Crochemore, L., Lindstr&amp;#246;m, G., and Arheimer, B.: Quantifying pluriannual hydrological memory with Catchment Forgetting Curves, &lt;em&gt;Hydrol. Earth Syst. Sci. Discuss.&lt;/em&gt; [preprint], in review, 2021.&lt;/p&gt;&lt;p&gt;Nicolle, P., Andr&amp;#233;assian, V., Royer-Gaspard, P., Perrin, C., Thirel, G., Coron, L., and Santos, L.: Technical note: RAT &amp;#8211; a robustness assessment test for calibrated and uncalibrated hydrological models, &lt;em&gt;Hydrol. Earth Syst. Sci.&lt;/em&gt;, 25, 5013&amp;#8211;5027, 2021.&lt;/p&gt;&lt;p&gt;Royer-Gaspard, P., Andr&amp;#233;assian, V., and Thirel, G.: Technical note: PMR &amp;#8211; a proxy metric to assess hydrological model robustness in a changing climate, &lt;em&gt;Hydrol. Earth Syst. Sci.&lt;/em&gt;, 25, 5703&amp;#8211;5716, 2021.&lt;/p&gt;