## WP-S5.1: Uncertainty of model results depending on input data

### Goals of the project:

Uncertainty in the input data leads to uncertain model results. The goal of this project is to let the users know the necessary accuracy of the input data according to their influence on the model output.

### Tasks of the project:

The tasks of WP-S5.1 are structured into the following sub-work packages with the following tasks:

**WP-S5.1.1: Studies for naturelike surfaces.**
In consultation with WP-S5.2 and PALM-4U users, we will identify which uncertainties in the results are still tolerable for users. The magnitude of the inherent errors in data collection is used as the bandwidth in the simulations in order to determine the resulting errors for nature-like surfaces.

**WP-S5.1.2: Studies for urban surfaces.**
In an urban environment, a large number of input variables have to be provided for the calculation of urban climate parameters.
Again, a systematic study determines the range of the simulation results to be expected against the background of the individual uncertainties of the input parameters.

**WP-S5.1.3: Studies for green and blue surfaces.**
Green elements in cities such as trees, facade greening, and water expanses are important elements for adapting the city to the consequences of climate change.
Also for these parameters the input variables are only available with more or less large uncertainties. Sensitivity studies determine how which parameters have to be available at what accuracy if a certain order of magnitude is expected in the result.

### Project structure:

PI: Prof. Dr. Günter Groß.

Project scientist: Simone Pfau, M.Sc.

### Deliverables:

Uncertainty and sensitivity analyses shall be performed to determine the bandwidth of the output data dependent on the uncertainty of the input data, to identify the parameters most responsible for the observed range of the outputs and to determine the necessary accuracy of input parameters to achieve a wanted accuracy in output.

### Progress so far:

The progress so far includes the selection of appropriate methods. For the uncertainty analysis, several input parameters shall be varied simultaneously. Because this leads to a number of model runs that is exponential in the number of input parameters, it is useful to screen out the parameters which do not have an important contribution to the uncertainty of the output. This will be done with the Morris method, which is currently being implemented. It requires a number of model runs that is linear in the number of inputs and is based on the idea that the difference between outputs with one different input factor is a measure for how sensitive the output is on this input factor. A number r of trajectories of sampling points is constructed in the parameter space, where two following points differ in only one input factor to calculate r measures for every input factor. The mean can be used to rank the input factors in order of importance for the uncertainty in the output. Additionally, Bayes’ approach will be used as an idea of how to estimate the allowed uncertainty in the input parameters to receive a wanted accuracy in the output. Here, a prior probability distribution which includes information on the input data is updated with a so called likelihood, the probability of getting a wanted output with a wanted spread given some input. This leads to a posterior distribution, which provides information about the variance of the input parameters given wanted properties of the model outputs. The next step is to complete the implementation of the Morris method and to apply it to a first exemplary area.

### References:

**Allmaras et al.:** Estimating parameters in physical models through Bayesian inversion a complete example, 2013.

**Campolongo et al.:** An effective screening design for sensitivity analysis of large models, 2006.

**Groß:** On the range of boundary layer model results depending on inaccurate input data, 2019.

**Hughes et al.:** Global sensitivity analysis of England's housing energy model, 2015.

**Laine et al.:** Ensemble prediction and parameter estimation system: the method, 2012.

**Lindauer:** Dynamische Sensitivitätsanalysemethoden energetischer Wohngebäudequartierssimulationen, 2017.

**Saltelli et al.:** Sensitivity Analysis in Praxtice, 2004.

**Soong-Oh Han:** Varianzbasierte Sensitivitätsanalyse als Beitrag zur Bewertung der Zuverlässigkeit adaptronischer Struktursysteme, 2011.

### Contacts:

gross[at]muk.uni-hannover.de

pfau[at]muk.uni-hannover.de