1. Facultad de Ingeniería, Centro de Cálculo
Application of ANN to the prediction of missing daily precipitation records, and comparison against linear methodologies
Carlos López-Vázquez
Facultad de Ingeniería, Centro de Cálculo
Montevideo URUGUAY

2. Organization of the presentation
The missing value problem
The experiment
Data and test area description
Methods tested
Results
Conclusions

3. The missing value problem
Weather records typically have missing values
Many applications require complete databases
Well established linear methods for interpolate spatial observations exist
Their performance is poor for daily rain records

4. The experiment
We created missing values at random locations in our dataset
We imputated them using all test methods
We computed RMS, mean and some percentiles of the absolute deviation between the original and the imputated value
We performed a number of simulations, and averaged the results

5. Data and test area description
20 years of daily records for 10 stations were available
30 % of the events have missing values
More than 80% of the readings are of zero rain, evenly distributed in the year
Annual averages ranges from 1600 to 500 mm/day; time correlation is low

6. Methods tested: linear
All follow the general equation
We restricted ourselves to weights w and bias b constant in time; its values depends on the method itself
Some commonly used methods will be briefly described
“Best among linear” methods can be obtained depending on the error measure used

7. Linear methods: Cressman
being
dij stands for the distance between station i and j
It does not use historical information
Only requires the station coordinates

8. Linear methods: Nearest neighbor
Uses only data from the closest available station
“closest” might be geometrical, or might be determined by an expert; we tested both
Due to its simplicity it is widely used

9. Linear methods: Optimum interpolation
It is the standard interpolation method in meteorology
It is also known as kriging in geostatistics
Requires the evaluation of the covariance matrix of the sample, and a model of the spatial correlation.
It is designed in order to minimize the expected RMSE

10. Linear methods: “The Best ones”
Given an objective measure of the error, it can be minimized by tuning the parameters w
Least sum of squares, Least average of the absolute error, Least 95 percentile, etc. are examples. The optimum might led to different vectors w in each case.
Calculating the parameters w might be a heavy nonlinear optimization problem

11. Non-linear methods: ANN
We used ANN as interpolators, with 9 inputs and 1 output
The training was performed with one third of the dataset using backpropagation and minimizing the RMSE
Some different architectures were considered (one and two hidden layers; different number of neurons, etc.) as well as some transformations of the data

12. Results
The results are poor, irrespective of the method; daily rain is a very difficult problem
Both ANN gave only slightly better results than linear methods, but were more robust
The training algorithm failed to escape from local minima; that leds to a significant CPU cost

13. Conclusions
Linear methods with constant coefficients have limited possibilities
Adding information of the day before improves to some extent the results
ANN gave interesting results, but with too much CPU requirements
Better training algorithms are required