--- title: Preliminary Results subject: Misc. Notes short_title: Experiment 1b - Spain (Time) authors: - name: J. Emmanuel Johnson affiliations: - CSIC - UCM - IGEO orcid: 0000-0002-6739-0053 email: juanjohn@ucm.es license: CC-BY-4.0 keywords: data --- * Duration? * Mean of Globe -> Correlated with Mean Location of Extremes # Metrics ## Log-Likelihood :::{list-table} Table with results for each model :header-rows: 1 :name: tb:madrid_unc_det_model * - Model - NLL - Error * - IID Model - -17089.15032017 - 4.06643326 * - Spatial Model - -16663.58281494 - 62.91590443 * - Temporal Model - -15571.70729426 - 4.73258625 * - Spatiotemporal Model - -15198.35183499 - 59.1095967 ::: ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ZYdGRfbmqLYnZl0lLtW-ZK75_DZ8shuN) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1HPknM6ouvWJLlFmhvN1NQqWPGdDIvVnv) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1-hemd578kUpwqLVeoguWH_ymrNoXbIpD) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1aY09hV62qzl4eBrGvrw0I9criNYGSE_2) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: *** # Parameters *** ## Location Parameter For the location parameter, recall the formulation $$ \boldsymbol{\mu}(t,\mathbf{s},\boldsymbol{\theta}) = \mu_0 + \mu_1t + \mu_2(\mathbf{s}) $$ So for this experiment, each model has a location bias parameter, $\mu_0$. However, the temporal model includes the location-bias parameter **and** the location-temporal weight parameter, $\mu_1$. In addition, the spatial model includes all parameters in the above equation. ### Location-Bias #### Histogram This is the histogram of **all samples** of the location-bias parameter, $\mu_0$, for each station in Spain. ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ETPsyh5_G-Dv3fKTWZz9iKC2ILe2a0_H) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Db4d9jAoqM30NWtNzFOIPt1S-Qnw-S__) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Z1GgqZtBN1THaQgA9av4hdwbEYXDVYUd) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: #### Mean Histogram This is the histogram of the **mean** of the location-bias parameter, $\mu_0$, for each station in Spain. ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1MPCdwBe-M5MvkqxyRI_0r4-cCbePIoRL) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ilEe51dIXLrmOjjvymcSqLfgEgLtrGUb) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=13wjIIL5RwmXD6mmcwwQwxGscPJ20j7oD) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: #### Maps ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1p4agHYmgP6-yocqc2Zs_Ro9ZGADrnvX_) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1mdhiYMycQzL-UTBtRj21mMdqNSxhdkTA) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1hhDqDRREyt1SgpYzppL0c6R-Zovx8eMd) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: *** ### Location Time-Weight We will look at the location temporal-weight parameter, $\mu_1$. This parameter dictates the positive (or negative) correlation between the time parameter and the location parameter. #### Histogram ::::{tab-set} :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1lblCWmiyMB8_zxMA5-t7aFo-b-IQf0oL) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1UT341gCM7IUL3WIgbyxSxZqp6Gpe3eaS) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: #### Mean Histogram ::::{tab-set} :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=17yUW3B0-5XiHWp3JLlwqqP_2gcPGfQ3o) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1o5SJWuQt2ye-QRfQU11oXHCQqbtLY8QO) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: #### Maps ::::{tab-set} :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1KmbfEneT1WNr3nQo-qlhD2FBGPm78Ss0) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1yrChIRrBiC4fD3OFriIp6nxAEBc7p1-n) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: *** ## Scale Recall, the parameterization for the scale parameter is given by $$ \sigma(t;\boldsymbol{\theta}) = \sigma_0 $$ where $\sigma_0$ is the scale parameter per station. This means that each model will have the same scale parameterization. ### Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ydWZ8t7nwerU1j4HBZVViZ730rjKehRq) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1PmzXiIo9YuzG43D1OXrj1lNzH6TnPS0Z) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Ex0nIdHLoNjSHPzBf0Zxd6RNQ4UBWvm4) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ### Mean Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=168lrD9uTqFb3eh2aPnqluUzrZ3nBOoBH) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1BuhwO4mBJqAwf1t4sXYftNVxEmMZd528) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1sa8DHfdpHnb43NVfWhtvkcLcaURrl0S4) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ### Map ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1UMxG73ietUXRG14NkL6ohaKrAI_r0RGN) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1xi6rCXMkm5dOtyPjVyyxFFFEFsnHl5wP) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1IbiXGHEXVwT2IfQ7fDoqRbdydQ63zhTi) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: *** ## Concentration Recall, the parameterization for the shape parameter is given by $$ \kappa(t;\boldsymbol{\theta}) = \kappa_0 $$ where $\kappa_0$ is the shape parameter per station. This means that each model will have the same shape parameterization. ### Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1t7uLs5KeHNIPVHNgcANBMBtFTg3h7Iy3) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1MDF-BxayRVC30t8RURiajhzgV-7YVdPh) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1I0e2jhk26ndVT8dncubV4Ugt84ZSHcKY) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ### Mean Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Pg0iC8ojjsDRImoAh2IDh262O7NfS2hQ) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1_LoVdtl9HVLumRkVh40cz59mLYAWyV05) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=11GOGQnVGbb79yRUyOmfAeDku0IgOvPqt) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ### Maps ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1G0vptzngPTjNKhJRFye_ecYK39264IYS) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1hSBbwS7tTOkQRWzYNCU9abZsunUvVzPB) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1vWyon_eAgICETmMw5XwRbbH65r77kAKh) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ## Rate We can relate the GEVD parameters to the GPD. This gives us a rate parameter, $\lambda$, which is the expected number of events that exceed some threshold, $y_0$, per year. $$ \lambda = \sigma + \kappa (y_0 - \mu) $$ However, we need to define an exceedence threshold, $y_0$. We will do a simple 95% quantile for each independent station with a declustering of 3 days. Then we can calculate the rate, $\lambda$. ### Threshold ::::{tab-set} :::{tab-item} Histogram :::{figure} :label: spain-threshold-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1OEYlNJhfFTju0wf0ag2TEp9dp6dHR1ZE) A histogram of the threshold parameter, $y_0$, for all stations. ::: :::{tab-item} Map :::{figure} :label: spain-threshold-map :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Gxr3ijb8O48LNYK9KZ2bj7Vh1QAE0giD) A map of the threshold parameter, $y_0$, for each station. ::: :::: ## Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1waVSFAlIQf14yZ-FigLTlXeRn-YZ-ORz) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1PxTtuJIEfMlv_f9Ki-WuRwmnXkpR_vsg) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=14eds2Go1w9z84aF6DbpJn9pFPUvNOcgN) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ## Mean Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1daA-VZ5eNwLo1MQJUjRdLLtFRTlE-Vyz) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1gGRxUeTYuzzQsiX07rw-bb67j12qi5Kh) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1u7br-b7uV6Fumj2XL5bkK3nJ4QeJTZgb) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ## Maps ### GMST - Scenario 0 ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Ij3ABiioK3MzgiEKGtz6wcAcUgBoAc-t) The return period for the iid model. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=167rTxyEvJeqHIxFs5knKqFRIJ9eEwQ1E) The return period under a GMST scenario 0 for the temporal model. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=16iCY2VbrYKSTK6CnhuBxDEyUKwal3eig) The return period under a GMST scenario 0 for the spatio-temporal model. ::: :::: ### GMST - Scenario 1 ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Ij3ABiioK3MzgiEKGtz6wcAcUgBoAc-t) The return period for the iid model. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1DysGvessTvfPyeTXgHevYUVOKHw3D-aX) The return period under a GMST scenario 1 for the temporal model. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1avezr6gTYUKZpRHEsGhgEFx6l2RRehCB) The return period under a GMST scenario 1 for the spatio-temporal model. ::: :::: ### GMST - Scenario 2 ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Ij3ABiioK3MzgiEKGtz6wcAcUgBoAc-t) The return period for the iid model. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1gk6WPrFpobNunZhgwuOc-8A0nwXCZlWY) The return period under a GMST scenario 2 for the temporal model. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1_kNaH9ix3C46HaBtcNoTDONoD-3Ilo1i) The return period under a GMST scenario 2 for the spatio-temporal model. ::: :::: # Returns ## Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1qTIOLXTGqVGWAyb06Opg439Wiv_rPQfx) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1Z-_eb9E67utNjyblXyIiKRFUxuV8q5CN) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1GyLcAmdU0UVEsuyIZ8pD5zXALEikfPsg) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=125SQgg4HoQ7EQl7V8PDm5OJm6_2dUysA) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ## Mean Histogram ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1bK_lk9ljehF8A6GIcA_hzXkHX9QaKAZG) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1sA7IqxZWSJH1EMMjzVGOgiE5mJ0ckLBR) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ccGszkmJBfELXrl-jKiEUaSOuu7dj3Xt) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1cyw2Ee2HMgbjPCVI4I9vkMwGlcuCkeJr) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: ## Maps ### GMST - Scenario 0 ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1_E4BavUauLsGKtUz9aS7O7ZcNNGd3nG-) The return period for the iid model. ::: :::{tab-item} Space :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1OgRoNPFMNesrp9pUb5wjMdvKZlz5r6BO) The return period under a GMST scenario 0 for the temporal model. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ReEWQx1xtmfGuxirb5OJYnI76dFJtjmu) The return period under a GMST scenario 0 for the temporal model. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ZH4rwPfTAO4_bhJSWo1SE6FZAGD91fnI) The return period under a GMST scenario 0 for the spatio-temporal model. ::: :::: ### GMST - Scenario 1 ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1fDiCsIbmCwvRkAzSj59V3U8SqXaHQO5g) The return period for the iid model. ::: :::{tab-item} Space :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1OgRoNPFMNesrp9pUb5wjMdvKZlz5r6BO) The return period under a GMST scenario 0 for the temporal model. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1ReEWQx1xtmfGuxirb5OJYnI76dFJtjmu) The return period under a GMST scenario 1 for the temporal model. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1B_egEwD6UtYQESGZK-7t7jaESSgj_jnB) The return period under a GMST scenario 1 for the spatio-temporal model. ::: :::: ### GMST - Scenario 2 ::::{tab-set} :::{tab-item} IID :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1fDiCsIbmCwvRkAzSj59V3U8SqXaHQO5g) The return period for the iid model. ::: :::{tab-item} Space :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1OgRoNPFMNesrp9pUb5wjMdvKZlz5r6BO) The return period under a GMST scenario 0 for the temporal model. ::: :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1eGyyILsEBBNonyTF4QkPHE54JNV50paE) The return period under a GMST scenario 2 for the temporal model. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1k0V1gRhGn1NgmPfNjioj5sjR_2rfNEPd) The return period under a GMST scenario 2 for the spatio-temporal model. ::: :::: ## Differences *** ### Case I - Scenario 0 and 1 The first case, we look at the absolute difference between the GMST scenarios 0 and 1. This corresponds to the difference in the pre-industrial climate and the actual climate. ::::{tab-set} :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1JqG7712s3by0kuBjH2wnBpUT7ef3I2j5) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=10_Vi6-f4RHycPlo0SxGBdZOZHuC399Ei) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::: *** ### Case I - Scenario 1 and 2s The first case, we look at the absolute difference between the GMST scenarios 1 and 2. This corresponds to the difference in the actual climate and the future climate. ::::{tab-set} :::{tab-item} Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1JQjjxuXY2zC1geWfAkaC0qFOXaS12tC0) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: :::{tab-item} Space-Time :::{figure} :label: madrid-t2m-hist :align: center ![Madrid Daily Maximum Temperature Time Series](https://drive.google.com/uc?id=1txc229DF80RiRzrmp5i9hJQlP35C3NgH) The negative log-likelihood loss (equation [](eq:madrid-gevd-mle-loss)) for each time step within the time series. ::: ::::