Stochastic modelling and prediction of monthly surface temperatures: StocSIPS
Authors: Del Rio Amador Lenin , Lovejoy Shaun 
Published: March 2020

&lt;p&gt;From hourly to decadal time scales, atmospheric fields are characterized by two scaling regimes: at high frequencies the weather, with fluctuations increasing with the time scale, and at low frequencies, macroweather with fluctuations decreasing with scale, the transition between the two at &lt;em&gt;&amp;#964;&lt;sub&gt;w&lt;/sub&gt;&lt;/em&gt;. This transition time is the lifetime of planetary structures and is therefore close to the deterministic predictability limit of conventional numerical weather prediction models. While it is thus the outer scale of deterministic weather models, conversely, it is the inner scale of stochastic macroweather models.&lt;/p&gt;&lt;p&gt;Here we explore the spatial dependence of this transition time. Starting at the surface (2m temperature) we found that the monthly average temperature falls in the macroweather regime for almost any location in the globe, except for parts of the tropical ocean where &lt;em&gt;&amp;#964;&lt;sub&gt;w &lt;/sub&gt;&lt;/em&gt;&amp;#8764; 1 - 2 years. As we increase in altitude, the dependence of &lt;em&gt;&amp;#964;&lt;sub&gt;w&lt;/sub&gt;&lt;/em&gt; with the location becomes more homogeneous and above 850mb &lt;em&gt;&amp;#964;&lt;sub&gt;w&lt;/sub&gt;&lt;/em&gt; &lt; 1 month almost everywhere. The longer tropical ocean transition scales are presumably the deterministic outer scales of the &amp;#8220;ocean weather&amp;#8221; regime.&lt;/p&gt;&lt;p&gt;Knowledge of &lt;em&gt;&amp;#964;&lt;sub&gt;w&lt;/sub&gt;&lt;/em&gt; is fundamental for stochastic macroweather forecasting.&amp;#160;&amp;#160; Such forecasting is based on symmetries, primarily the power-law behavior of the fluctuations that implies a huge memory that can be exploited for forecasts up to several years. In addition, there is another approximate symmetry called &amp;#8220;statistical space-time factorization&amp;#8221; relating spatial and temporal statistics. Finally, while weather regime temperature fluctuations are highly intermittent, in macroweather the intermittency is much lower, fluctuations are quasi Gaussian.&lt;/p&gt;&lt;p&gt;The Stochastic Seasonal and Interannual Prediction System (StocSIPS&lt;sup&gt;[1,2]&lt;/sup&gt;) is a stochastic data-driven model that exploits these symmetries to perform macroweather (long-term) forecasts. Compared to traditional global circulation models (GCM), it has the advantage of forcing predictions to converge to the real-world climate (not the model climate). It extracts the internal variability (weather noise) directly from past data and does not suffer from model drift. Some other practical advantages include much lower computational cost, no need for downscaling and no ad hoc postprocessing.&lt;/p&gt;&lt;p&gt;We show that StocSIPS can predict monthly average surface temperature (nearly) to its stochastic predictability limits. Using monthly to annual lead time hindcasts, we compare StocSIPS predictions with those from the CanSIPS&lt;sup&gt;[3]&lt;/sup&gt; GCM. Beyond a month, and especially over land, StocSIPS generally has higher skill. For regular StocSIPS forecasts, see http://www.physics.mcgill.ca/StocSIPS/.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;&lt;sup&gt;[1]&lt;/sup&gt; Del Rio Amador, L. and Lovejoy, S. (2019) Clim Dyn, &lt;strong&gt;53&lt;/strong&gt;: 4373. https://doi.org/10.1007/s00382-019-04791-4&lt;/p&gt;&lt;p&gt;&lt;sup&gt;[2]&lt;/sup&gt; Lovejoy, S., Del Rio Amador, L., H&amp;#233;bert, R. (2017) In Nonlinear Advances in Geosciences, A.A. Tsonis ed. Springer Nature, 305&amp;#8211;355 DOI: 10.1007/978-3-319-58895-7&lt;/p&gt;&lt;p&gt;&lt;sup&gt;[3]&lt;/sup&gt; Merryfield WJ, Denis B, Fontecilla JS, Lee WS, Kharin S, Hodgson J, Archambault B (2011) Rep., 51pp, Environment Canada.&lt;/p&gt;