Tuomo Kauranne

Algorithm for Extracting Digital Terrain Models under Forest Canopy from Airborne LiDAR Data

Extracting digital elevationmodels (DTMs) from LiDAR data under forest canopy is a challenging task. This is because the forest canopy tends to block a portion of the LiDAR pulses from reaching the ground, hence introducing gaps in the data. This paper presents an algorithm for DTM extraction from LiDAR data under forest canopy. The algorithm copes with the challenge of low data density by generating a series of coarse DTMs by using the few ground points available and using trend surfaces to interpolate missing elevation values in the vicinity of the available points. This process generates a cloud of ground points from which the final DTM is generated. The algorithm has been compared to two other algorithms proposed in the literature in three different test sites with varying degrees of difficulty. Results show that the algorithm presented in this paper is more tolerant to low data density compared to the other two algorithms. The results further show that with decreasing point density, the differences between the three algorithms dramatically increased from about 0.5m to over 10m.

Estimating the number of clusters in a numerical data set via quantization error modeling

In this paper, we consider the problem of unsupervised clustering (vector quantization) of multidimensional numerical data. We propose a new method for determining an optimal number of clusters in the data set. The method is based on parametric modeling of the quantization error. The model parameter can be treated as the effective dimensionality of the data set. The proposed method was tested with artificial and real numerical data sets and the results of the experiments demonstrate empirically not only the effectiveness of the method but its ability to cope with difficult cases where other known methods fail. A parameterized model for the clustering error is introduced.The model parameter is a measure of the data dimension and homogeneity.A new cost criterion is derived from the properties of the model.The method demonstrates good results for numerical data sets.

Linear Models for Airborne-Laser-Scanning-Based Operational Forest Inventory With Small Field Sample Size and Highly Correlated LiDAR Data

Modern operational forest inventory often uses remotely sensed data that cover the whole inventory area to produce spatially explicit estimates of forest properties through statistical models. The data obtained by airborne light detection and ranging (LiDAR) correlate well with many forest inventory variables, such as the tree height, the timber volume, and the biomass. To construct an accurate model over thousands of hectares, LiDAR data must be supplemented with several hundred field sample measurements of forest inventory variables. This can be costly and time consuming. Different LiDAR-data-based and spatial-data-based sampling designs can reduce the number of field sample plots needed. However, problems arising from the features of the LiDAR data, such as a large number of predictors compared with the sample size (overfitting) or a strong correlation among predictors (multicollinearity), may decrease the accuracy and precision of the estimates and predictions. To overcome these problems, a Bayesian linear model with the singular value decomposition of predictors, combined with regularization, is proposed. The model performance in predicting different forest inventory variables is verified in ten inventory areas from two continents, where the number of field sample plots is reduced using different sampling designs. The results show that, with an appropriate field plot selection strategy and the proposed linear model, the total relative error of the predicted forest inventory variables is only 5%-15% larger using 50 field sample plots than the error of a linear model estimated with several hundred field sample plots when we sum up the error due to both the model noise variance and the models lack of fit.

Moving Voxel Method for Estimating Canopy Base Height from Airborne Laser Scanner Data

Canopy base height (CBH) is a key parameter used in forest-fire modeling, particularly crown fires. However, estimating CBH is a challenging task, because normally, it is difficult to measure it in the field. This has led to the use of simple estimators (e.g., the average of individual trees in a plot) for modeling CBH. In this paper, we propose a method for estimating CBH from airborne light detection and ranging (LiDAR) data. We also compare the performance of several estimators (Lorey’s mean, the arithmetic mean and the 40th and 50th percentiles) used to estimate CBH at the plot level. The method we propose uses a moving voxel to estimate the height of the gaps (in the LiDAR point cloud) below tree crowns and uses this information for modeling CBH. The advantage of this approach is that it is more tolerant to variations in LiDAR data (e.g., due to season) and tree species, because it works directly with the height information in the data. Our approach gave better results when compared to standard percentile-based LiDAR metrics commonly used in modeling CBH. Using Lorey’s mean, the arithmetic mean and the 40th and 50th percentiles as CBH estimators at the plot level, the highest and lowest values for root mean square error (RMSE) and root mean square error for cross-validation (RMSEcv) and R2 for our method were 1.74/2.40, 2.69/3.90 and 0.46/0.71, respectively, while with traditional LiDAR-based metrics, the results were 1.92/2.48, 3.34/5.51 and 0.44/0.65. Moreover, the use of Lorey’s mean as a CBH estimator at the plot level resulted in models with better predictive value based on the leave-one-out cross-validation (LOOCV) results used to compute the RMSEcv values.

The multiple-mean-reversion jump-diffusion model for Nordic electricity spot prices

Electricity spot market prices are notoriously difficult to model, let alone predict, because of their extreme volatility. Such volatility is reflected in so-called price spikes that may increase the spot price by an order of magnitude as a matter of hours. Spot market price series are also subject to many other types of phenomena, such as periodicities at different scales, and to mean reversion. We introduce a model for electricity spot market prices that includes both spikes and mean reversion. The model is based on a jump diffusion process that is superimposed on a mean reverting Ornstein-Uhlenbeck model. Mean reversion takes place at several different time and price scales, so as to reproduce the observed behavior of spot market prices correctly. The parameters of the model are calibrated with the Nord Pool spot market hourly price series using a maximum likelihood approach. The simulated price series thus obtained very closely follows the statistical characteristics of the real price series.

Unsupervised segmentation and approximation of digital curves with rate-distortion curve modeling

This paper considers the problem of unsupervised segmentation and approximation of digital curves and trajectories with a set of geometrical primitives (model functions). An algorithm is proposed based on a parameterized model of the Rate-Distortion curve. The multiplicative cost function is then derived from the model. By analyzing the minimum of the cost function, a solution is defined that produces the best possible balance between the number of segments and the approximation error. The proposed algorithm was tested for polygonal approximation and multi-model approximation (circular arcs and line segments for digital curves, and polynomials for trajectory). The algorithm demonstrated its efficiency in comparisons with known methods with a heuristic cost function. The proposed method can additionally be used for segmentation and approximation of signals and time series. A new algorithm for unsupervised segmentation of digital curves is introduced.This method gives solutions with the best balance between error and description length.A multiplicative criterion for evaluation of solutions is introduced.

The impact of emissions trading on electricity spot market price behavior

Purpose – Under the Kyoto protocol, emissions trading was imposed upon the Nordic Nord Pool Spot market in 2005. The purpose of this paper is to identify and characterize an important side‐effect of emissions trading on electricity spot market price behavior by statistically comparing price behavior before and after emissions trading was introduced.Design/methodology/approach – The analysis is based on an analysis of the skill of regression models in explaining price behavior before and after 2005.Findings – It turns out that regression models based on background variables such as temperature, water reservoir levels, and even the price of emission rights themselves lose much of their skill from 2005 onwards. The histogram of the residual time series of an optimally calibrated regression model demonstrates a considerably more “fat‐tailed” behavior after 2005, with a much higher volatility and reduced amenability for regression by background variables.Practical implications – The results point to an increas...

Multi-Agent Stochastic Simulation for the Electricity Spot Market Price

The Great Recession of 2008-2009 has dented public confidence in econometrics quite significantly, as few econometric models were able to predict it. Since then, many economists have turned to looking at the psychology of markets in more detail. While some see these events as a sign that economics is an art, rather than a science, multi-agent modelling represents a compromise between these two worlds. In this article, we try to reintroduce stochastic processes to the heart of econometrics, but now equipped with the capability of simulating human emotions. This is done by representing several of Keynes’ Animal Spirits with terms in ensemble methods for stochastic differerential equations. These terms are derived from similarities between fluid dynamics and collective market behavior. As our test market, we use the price series of the Nordic electricity spot market Nordpool.

Long-distance multistatic aircraft tracking with VHF frequency doppler effect

A multistatic Doppler radar concept based on long-distance VHF frequency recordings is presented and tested in a two-receiver, one-transmitter configuration. The core of the method is a mathematical model of Doppler shift generation in a passive configuration of many simultaneous transmitting radio stations and receivers that share the Doppler shift information they have recorded. The tracking capabilities of such a multistatic configuration are tested in an off-line experiment over a distance of 400 km. Aircraft position was recovered to an apparent precision of 1500 m. The method also corrects for errors in time synchronization between receivers.

LiDAR-Assisted Multi-Source Program (LAMP) for Measuring Above Ground Biomass and Forest Carbon

Forest measurement for purposes like harvesting planning, biomass estimation and mitigating climate change through carbon capture by forests call for increasingly frequent forest measurement campaigns that need to balance cost with accuracy and precision. Often this implies the use of remote sensing based measurement methods. For any remote-sensing based methods to be accurate, they must be validated against field data. We present a method that combines field measurements with two layers of remote sensing data: sampling of forests by airborne laser scanning (LiDAR) and Landsat imagery. The Bayesian model-based framework presented here is called Lidar-Assisted Multi-source Programme—or LAMP—for Above Ground Biomass estimation. The method has two variants: LAMP2 which splits the biomass estimation task into two separate stages: forest type stratification from Landsat imagery and mean biomass density estimation of each forest type by LiDAR models calibrated on field plots. LAMP3, on the other hand, estimates first the biomass on a LiDAR sample using models calibrated with field plots and then uses these LiDAR-based models to generate biomass density estimates on thousands of surrogate plots, with which a satellite image based model is calibrated and subsequently used to estimate biomass density on the entire forest area. Both LAMP methods have been applied to a 2 million hectare area in Southern Nepal, the Terai Arc Landscape or TAL to calculate the emission Reference Levels (RLs) that are required for the UN REDD+ program that was accepted as part of the Paris Climate Agreement. The uncertainty of these estimates is studied with error variance estimation, cross-validation and Monte Carlo simulation. The relative accuracy of activity data at pixel level was found to be 14 per cent at 95 per cent confidence level and the root mean squared error of biomass estimates to be between 35 and 39 per cent at 1 ha resolution.