Nan Wang , Luigi Lombardo , Weiming Cheng , Mattia Marconcini , Felix Bachofer , Liang Guo, Junnan Xiong 

Hydro-morphological processes (HMP; any process in the spectrum between debris flows and flash floods) threaten human infrastructures and lives; and their effects are only expected to worsen in the context of climate change. One of the ways to limit the potential damage of HMP is to take preventive or remedial actions probabilistically knowing where and how frequently they may occur. The expected information on where and how frequently a given earth surface process may manifest itself is referred to as susceptibility. And, for the whole Chinese territory, a susceptibility model for HMP is currently not available.

To address this issue, we propose a yearly space-time model consisting of a Generalized Linear Model of the binomial family. The target variable of such model is the annual presence/absence information of HMP per catchment across China, from 1985 to 2015. This information has been accessed via the Chinese catalogue of HMP, a data repository the Chinese government has activated in 195X and which is still currently in use. This binary spatio-temporal information is regressed against a set of time-invariant (catchment shape indices and terrain attributes) and time-variant (urban coverage, rainfall, vegetation density and land use) covariates. Furthermore, we include a regression constant for each of the 31 years under consideration and also a three-years aggregated information on previously occurred (and not-occurred) HMP.
We consider two versions of our modeling approach, an explanatory benchmark where we fit the whole space-time HMP data, including a multiple intercept per year. Furthermore, we also extend this explanatory model into a predictive one, by considering four temporal cross-validation schemes (Forward-All, Forward-Sequence, Backward-All, and Backward-Sequence), removing the yearly multiple intercept. In the first of 31 temporal replicates, Forward-All is calibrated for 1985 and then used to predict from 1986 to 2015. In the second step, a model is calibrated for 1985 and 1986 combined and used to validate the rest of the space-time series. This is replicated up to the last model where the combined data from 1985 to 2014 is calibrated to predict the last year of the HMP presence/absence data. Forward-Sequence also moves in the same temporal direction but the sampling scheme sequentially extracts two years at a time, one for calibration and one for validation. For instance, the first step is trained for 1985 and used to predict 1986; then the second step is trained for 1986 and used to predict 1987. As for Backward-All, and Backward-Sequence, their structure is the same but the temporal direction goes from 2015 to 1985.

Our explanatory model suggests that the overall number of HMP events per year has increased in the last decade and that the annual susceptibility has subsequently followed the same trend.
As for the four cross-validation routines, Forward-Sequence shows excellent performance with an average AUC of 0.83, slightly better than Forward-All, Backward-All, and Backward-Sequence. From an interpretative standpoint, this implies that the best spatio-temporal prediction we obtained is associated with short-term variations of the HMP distribution and that such variations should be considered in a forward temporal direction.

Furthermore, we portrayed the annual susceptibility models into 30 maps, where the south-east of China is shown to exhibit the largest variation in the spatio-temporal probability of HMP occurrence. Also, we compressed the whole spatio-temporal prediction into three summary maps. These report the mean, maximum and 95\% confidence interval of the spatio-temporal susceptibility distribution per catchment, per year.

The information we present has a dual value. On the one hand, we provide a platform to interpret environmental effects on HMP at a very large scale, both spatially (the whole Chinese country) and temporally (31 years of records). On the other hand, we provide information on which catchments are more prone to experience a HMP-driven disaster. Hence, a step further would be to select the more susceptible catchment for detailed analysis where physically-based models could be tested to estimate the potentially impacted areas.