El Modelo de Solow

After extracting the signal of the weather phenomenon from the observations in an au- tomatic way, it is possible to build the verification dataset, against which to compare the probabilistic forecasts calculated with two different methodologies, as explained in the previous sections.

The general aim of our analysis is to calculate two scores from the probabilistic verifi- cation, then calculate the differences and assess whether any difference in the scores is significant. A null hypothesis of no difference between the two probabilistic forecasts is used to test significance.

In regard to the scores Ignorance score, the Brier Score and the Area under the ROC curve (AUC) are calculated. This provides information about reliability and resolution (discussed in chapter 5) and focusses on additional useful information provided by the convection-permitting ensemble forecast.

In order to calculate any significance in the verification scores difference (Information gain, Brier score difference and AUC difference) two different techniques are considered. For the probabilistic scores, the empirical bootstrap technique is used. Nboot sequences of the forecast-observation pair are considered, each one obtained from the original by sampling with replacement. Then the Information gain and Brier Score difference are computed for each sequence and finally the 95% confidence interval.

In regard to the comparison of the area under the ROC curve, since in this case the areas are correlated, the method described in (DeLong et al.,1988) to compute the variance is used. Then, following (Zhou et al.,2008) a Z-test is used to compare the two areas under the ROC curves and to test the null hypothesis the two probabilistic forecasts having the same AUC.

Chapter 4

Probabilistic forecasts of sea breezes

In this chapter the information about sea-breeze occurrence is first extracted from a dy- namically downscaled convection-permitting ensemble forecast (CP-EPS) using a novel automatic tracking algorithm and then compared with a Bayesian model, taking as input coarser resolution data and trained on convective-scale data.

In essence the Bayesian method forecasts the high resolution member based on large- scale variables from low resolution model (LR-EPS). The aim of this is twofold: -firstly to develop a method to extract information from the low resolution prior to the running of the convective-scale forecast for real time forecasting ; secondly to provide an estimate of the information gained by running the convective-scale forecast beyond that which is contained in the large-scale flow conditions.

The work presented in this chapter is part of a paper which is published in the Quarterly Journal of the Royal Meteorological Society, with the reference:

Cafaro C, Frame THA, Methven J, Roberts N, Bröcker J, (2019). The added value of convection-permitting ensemble forecasts compared to a Bayesian forecast driven by the global ensemble. Q. J. R. Met. Soc., doi:10.1002/qj.3531

The research included in this paper was conducted by the main author under the super- vision of T. H. A. Frame, J. Methven, N. Roberts and J. Bröcker via weekly meetings and discussions. The lead author wrote the first draft of the paper, prepared all the figures and had overall control of the submitted paper. The other authors commented on draft version of the paper and the lead author updated the manuscript accordingly.

4.1

Introduction

The sea breeze is a phenomenon that has been known about long time, already docu- mented by Aristotle (seeNeumann(1973) and references therein). Yet it still raises inter- esting open questions, in particular about how it is identified and predicted.

A sea breeze is a mesoscale circulation caused by the temperature contrast between the land and the sea during the day, i.e. the differential heating due to different heat capacity of the water and land. Land heats more quickly during the day and cools more quickly at night. Sea breezes are an appealing choice of phenomena for model comparison because they are geographically constrained to initiate at the coast and occur quite frequently in summer months. Also, sea breeze forecasting is important for several reasons: its im- pacts on air quality, , since it affects transports of pollutants e.g. (Loughner et al., 2014; Kambezidis et al.,1998;Clappier et al.,2000). It is also important for health, being a relief

FIGURE 4.1: Percentage of publications every 10 years years since 1950 (up to 18 December 2018) including the phrase “sea breeze” according to Google Scholar for four journals (BAMS, JAS , MWR, QJRMS). Each dot represents the percentage in the following 10 years (except for year 2010).

from oppressive hot weather (e.g. Papanastasiou et al.(2010);Meir et al.(2013)) and as a possible trigger for convective storms or enhancing rainfall totals from existing storms, especially when interacting with other mesoscale flows (Warren,2014;Birch et al.,2015). Miller et al.(2003) stated that forecasting sea breezes consists of three main aspects: oc- currence, propagation speed and direction and distance of penetration. In this study the main focus is on the occurrence. Other sea breeze characteristics are examined in the sec- tion 4.6.

Furthermore, this analysis can benefit from the fact there have been lots of studies on the sea breeze, especially in the past 40 years (see figure 4.1), as more and more people are living coastal urban areas. Among these studies,Azorin-Molina and Tijm(2011, Table 1) include a list of studies on sea breeze forecasting andCrosman and Horel(2010, Table 1) on sea breeze numerical studies). This has permitted to understand the phenomena, how best to detect it and what drives it.

For instance,Miller et al.(2003, Table 3) presents a list of factors controlling the sea-breeze occurrence and inland penetration. The correct representation of these factors in NWP models depend on the model grid size. In particular, topography, shape of the coastline require fine grid scale to be properly represented. This is crucial to reduce forecast errors (e.g.Persson and Grazzini(2007) reports an “over-sized”1sea breeze during the forecast integration, due to the grid box size of 25 km of the ECMWF model).

Since sea breezes usually occur on a time scale of about 1 day and spatial scale between

1_{This is directly quoted from the authors’ document. Over-sized in this context could mean a sea-breeze}

10 to 100 km (Lin,2007), it is not expected that coarse resolution model (with grid spac- ing larger than 20 km) are able to properly resolve the sea breeze circulation. The key distinction being that the CP-EPSs can explicitly develop a sea breeze, whereas the global ensemble can only predict the large-scale conditions that give rise to sea breeze.

In this study the degree to which CP-EPSs provide additional information about the oc- currence of sea-breeze beyond that which could be determined from the larger-scale envi- ronment is examined. This means to post-process direct model output variables to extract information and create a “sea breeze occurrence” variable based on them.

The information extracted from a CP-EPS is compared with a Bayesian model based on LR-EPS model variables. The Bayesian model should perform better than the LR-EPS alone and is still cheap compared to running a CP-EPS, and therefore provides a much more stringent test of the benefit of the CP-EPSs, compared with a more intelligent use of the LR-EPSs than simply extracting raw model output.

Although the sea breeze is locally forced by the land-sea temperature contrast, the syn- optic scale flow plays a fundamental role in controlling the initiation and the evolution of the sea breeze itself. There are of course other geographical factors involved, like coast- line topography, surface roughness, latitude, season. HoweverAzorin-Molina and Chen (2008) deem the impact of the large-flow to be greater than these, even than the thermal gradient. This is related to question the source of sea-breeze predictability. More pre- cisely it is assessed whether sea-breeze occurrence is due to better representation of local factors and sea-breeze dynamics in CP-EPSs or if it can be instead derived solely from the knowledge of the most influential large-scale conditions (synoptic wind and land-sea temperature contrast) which are sufficiently well represented even on coarse grid boxes. These are used as predictors in the Bayesian model.

In this context ensembles are used mainly for two reasons: they provide inherent uncer- tainty in initiation and subsequent development because of dependence on environmen- tal factors that are themselves open to uncertainty; they provide a larger sample to get a more robust comparison between the two forecasting approaches. Therefore a more appropriate question to answer is “how much more information is the CP-EPS bringing compared to the LR-EPS and is this significant ?”. The null hypothesis is that the two EPSs provide the same amount of information. Therefore sea breeze occurrence becomes a test, by which this hypothesis can be either rejected or accepted.

The rest of the chapter is organized into five sections. In section 4.2 the forecast and ob- servational data used are described, section 4.3 presents the method for identifying sea breezes in observations and CP-EPSs and the Bayesian model, section 4.4 contains a first qualitative comparison between the two probabilistic forecasts and subjective verifica- tion against station observations. A summary of the results and conclusions is given in section 4.7.