From eb1ef925b2e998795c409cc81c2291f53e21c3eb Mon Sep 17 00:00:00 2001 From: Feiyu Lu Date: Mon, 17 Jul 2023 21:23:20 -0400 Subject: [PATCH 01/10] Adding description of DA --- notebooks/DA_demo_L96.ipynb | 56 ++++++++++++++++++++++++++++++++---- notebooks/figs/DA_step.png | Bin 0 -> 368756 bytes 2 files changed, 51 insertions(+), 5 deletions(-) create mode 100644 notebooks/figs/DA_step.png diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 37d6e61a..611ed9df 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -44,6 +44,52 @@ "```" ] }, + { + "cell_type": "markdown", + "id": "c33e3435", + "metadata": {}, + "source": [ + "# What is DA? Why do we do it?\n", + "\n", + "Data assimilation is an approach for combining data (observations) with prior knowledge (from a physical model) to obtain an estimate of the true state of a system. We use data assimilation to generate accurate initial conditions for weather and climate predictions, and to produce reanalysis products (state estimates) of the atmosphere-ocean-sea ice-land system. \n", + "\n", + "Conceptually, data assimilation follows the Bayes' Rule:\n", + "\n", + "\\begin{align}\n", + "\\ P(X|Obs)=\\frac{P(Obs|X)P(X)}{P(Obs)}\n", + "\\end{align}\n", + "\n", + "where $P(X|Obs)$ is the posterior distribution, or the analysis in DA terms, and $P(X)$ is the prior distribution, or the forecast in DA terms. $P(Obs|X)$ is the observation distribution given the prior. Below is a simple schematic representation of one DA step.\n", + "\n", + "```{figure} figs/DA_step.png\n", + "```\n" + ] + }, + { + "cell_type": "markdown", + "id": "208a8f14", + "metadata": {}, + "source": [ + "# Design of the data assimilation experiments in L96\n", + "\n", + "We use the 2-scale L96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". This is what we call an idealized biased-model framework in DA research. Our DA model is biased compared to our truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", + "\n", + "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", + "1. Generate a “truth” signal from 2-scale L96 model\n", + "2. Specify a biased “GCM”model for performing DA\n", + " * Choose P (to start, use GCM with P=0).\n", + " * Choose F_GCM (to start, use F_GCM=F).\n", + "3. Collect sparse and noisy observations, sampled from “truth”\n", + " * Specify observation density in space, frequency in time\n", + " * Specify observational error\n", + "4. Perform DA using a method of choice\n", + " * Choose DA method: EnKF, 3DVAR, Hybrid EnKF\n", + " * Specify DA setup: ensemble members, localization, inflation\n", + "5. Assess DA performance\n", + " * RMSE of DA experiment relative to truth\n", + "6. Analyze DA increments to assess GCM model error (optional)\n" + ] + }, { "cell_type": "markdown", "id": "66584b6f", @@ -96,11 +142,11 @@ " seasonal = False # Option for adding a seasonal cycle to the forcing in the L96 truth model\n", " B_loc = 5 # Spatial localization radius for DA\n", " DA = \"EnKF\" # DA method\n", - " nens = 100 # Number of ensemble members for DA\n", + " nens = 500 # Number of ensemble members for DA\n", " inflate_opt = \"relaxation\" # Method for DA model covariance inflation\n", - " inflate_factor = 0.2 # Inflation factor\n", - " hybrid_factor = 0.1 # Inflation factor for hybrid EnKF method\n", - " param_DA = False # Switch to parameter estimation with DA\n", + " inflate_factor = 0.65 # Inflation factor\n", + " hybrid_factor = 0.1 # Weighting factor for hybrid EnKF method (weight of static B matrix)\n", + " param_DA = False # Switch to turn on parameter estimation with DA\n", " param_sd = [0.01, 0.02, 0.1, 0.5] # Polynomal parameter standard deviation\n", " param_inflate = \"multiplicative\" # Method for parameter variance inflation\n", " param_inf_factor = 0.02 # Parameter inflation factor\n", @@ -1140,7 +1186,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.8.12" } }, "nbformat": 4, diff --git a/notebooks/figs/DA_step.png b/notebooks/figs/DA_step.png new file mode 100644 index 0000000000000000000000000000000000000000..937fecb9d7f5888530369757c5cec0dba408c1c1 GIT binary patch literal 368756 zcmeFZXIN9));3I&q6i2|kwB0ZkPZp~LO?+fsfyC27m<#%&=Dje9i&NBL_~V;HFN}| zBR%w9LJjp>>~r?ndamd3{rmlR;KHonTr+cyIm$i8Jr;qg%5qmP-@J^2gL75>q0AE; z970AM90Dd{Lf|)amF#@L3+}5Ya`$m^yFtsq8-G(xc{3#?oZG-PG0r7iN*w%)A;32d z?oFIae_i9?Ji?{_&-D{rj(?BA!@)sX;1K+Kj5hFk@f8F70C)fU6+adCpBYo}{vJ)p zn2P`RH31Va8b@fgA^~_Iv3scX3I~UV^5O^AJf#oVf)tLt%)O_sxN9{?uetJQq(ZZD zR8mokMbeOc&A!`?_;^NDk6lW`vCh~ksKtU|m~oN66yg}Ey*wkm%=fYP*^^Ax==RS3`WfN@W*}VVz z@V_Q80O5L&W|wsyWxRRw#$85xK}9Q>XH~BA=zPt(taJaK*7N`Qv;OnjdMMuTBPOqa 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zMZ>-|MAFG{+3oNsXEqaSqU(B*^$&0S8`B83wanhv5+)XQFC}BHc^lc=fsOCL&U9d{ zJFwu6Db;_P;omp~7}qtPtrR=k>#gZ=80$c%Eq4ueHu-?Vk9N(Q@fdI%=3Ga^R_1^F z^S+zmR`2(Y0D`_fmL>4|5|#92AHHXY>mGr){Dp0IpD~EkAMo_Y$b_hvB1kN3zlrrg zB)++I##y{sspD3p25-@yF~>hwNy5h4$MO>AOUYKRvEp$H`7bbVDhRJV3!yXi*a+YI S3Oxn Date: Wed, 19 Jul 2023 16:20:09 -0400 Subject: [PATCH 02/10] Moved DA-related functions to DA_methods.py. Added additional descriptions. --- notebooks/DA_demo_L96.ipynb | 289 ++++-------------------------------- notebooks/DA_methods.py | 119 ++++++++++++++- 2 files changed, 144 insertions(+), 264 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 611ed9df..cfaf1a9b 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -8,42 +8,6 @@ "# Data Assimilation demo in the Lorenz 96 (L96) two time-scale model\n" ] }, - { - "cell_type": "markdown", - "id": "4c383a2a", - "metadata": {}, - "source": [ - "# Recap of L96 and notation" - ] - }, - { - "cell_type": "markdown", - "id": "2b0a10bb", - "metadata": { - "user_expressions": [] - }, - "source": [ - "{cite}`Lorenz1995` describes a two-time scale dynamical system using two equations which are:\n", - "\n", - "\\begin{align}\n", - "\\frac{d}{dt} X_k\n", - "&= - X_{k-1} \\left( X_{k-2} - X_{k+1} \\right) - X_k + F - \\left( \\frac{hc}{b} \\right) \\sum_{j=0}^{J-1} Y_{j,k}\n", - "\\\\\n", - "\\frac{d}{dt} Y_{j,k}\n", - "&= - cbY_{j+1,k} \\left( Y_{j+2,k} - X_{j-1,k} \\right) - c Y_{j,k} + \\frac{hc}{b} X_k\n", - "\\end{align}\n", - "\n", - "where $X_k$, $k=0,\\ldots,K-1$, denotes the _large scale_ with $K$ degrees of freedom. The $k$ index is periodic, meaning $k=K$ is referring to $k=0$, $k=-1$ is referring to $k=K-1$, and so on. The $j$ indices represent a sub-division of each $k$-element denoting that the $J$ $Y$-values are coupled to a single $X$ value. When $(j+1,k)$ refers to a value beyond $J$, it cycles and refers back to the first value $(1,k+1)$. The slow time-scale queation is forced by the parameter $F$, which determines the chaotic behaviour of the system {cite}`Wilks2005`. The overall structure is illustrated in Fig. 1.\n", - "\n", - "\n", - "```{figure} https://www.researchgate.net/publication/319201436/figure/fig1/AS:869115023589376@1584224577926/Visualisation-of-a-two-scale-Lorenz-96-system-with-J-8-and-K-6-Global-scale-values.png\n", - ":width: 400px\n", - ":name: l96-equation-figure-da-demo\n", - "\n", - "*Visualisation of a two-scale Lorenz '96 system with J = 8 and K = 6. Global-scale variables ($X_k$) are updated based on neighbouring variables and on the local-scale variables ($Y_{j,k}$) associated with the corresponding global-scale variable. Local-scale variabless are updated based on neighbouring variables and the associated global-scale variable. The neighbourhood topology of both local and global-scale variables is circular. Image from [Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures - Scientific Figure on ResearchGate.](https://www.researchgate.net/figure/Visualisation-of-a-two-scale-Lorenz-96-system-with-J-8-and-K-6-Global-scale-values_fig1_319201436)*.\n", - "```" - ] - }, { "cell_type": "markdown", "id": "c33e3435", @@ -51,7 +15,7 @@ "source": [ "# What is DA? Why do we do it?\n", "\n", - "Data assimilation is an approach for combining data (observations) with prior knowledge (from a physical model) to obtain an estimate of the true state of a system. We use data assimilation to generate accurate initial conditions for weather and climate predictions, and to produce reanalysis products (state estimates) of the atmosphere-ocean-sea ice-land system. \n", + "Data assimilation is an approach for combining data (e.g. observations) with prior knowledge (e.g. from a physical model) to obtain an estimate of the true state of a system. We use data assimilation to generate accurate initial conditions for weather and climate predictions, and to produce reanalysis products (state estimates) of the atmosphere-ocean-sea ice-land system. \n", "\n", "Conceptually, data assimilation follows the Bayes' Rule:\n", "\n", @@ -59,7 +23,7 @@ "\\ P(X|Obs)=\\frac{P(Obs|X)P(X)}{P(Obs)}\n", "\\end{align}\n", "\n", - "where $P(X|Obs)$ is the posterior distribution, or the analysis in DA terms, and $P(X)$ is the prior distribution, or the forecast in DA terms. $P(Obs|X)$ is the observation distribution given the prior. Below is a simple schematic representation of one DA step.\n", + "where $X$ is the state of the dynamic system, $P(X|Obs)$ is the posterior distribution, or the analysis in DA terms, and $P(X)$ is the prior distribution, or the forecast in DA terms. $P(Obs|X)$ is the observation distribution given the prior. Simply speaking, we want to know the best estimate of the current state $X$ of the system given the available observations. Below is a simple schematic representation of one DA step.\n", "\n", "```{figure} figs/DA_step.png\n", "```\n" @@ -72,7 +36,7 @@ "source": [ "# Design of the data assimilation experiments in L96\n", "\n", - "We use the 2-scale L96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". This is what we call an idealized biased-model framework in DA research. Our DA model is biased compared to our truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", + "We use the 2-scale Lorenz-96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". Detailed description of this setup can be find here (https://m2lines.github.io/L96_demo/notebooks/gcm-analogue.html). This is what we call an idealized biased-model framework in DA research, in the sense that our DA model is biased compared to the truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", "\n", "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", "1. Generate a “truth” signal from 2-scale L96 model\n", @@ -95,7 +59,7 @@ "id": "66584b6f", "metadata": {}, "source": [ - "# 1. Define variables and functions to use throughout notebook" + "# 1. Define our \"GCM\" and DA parameters to use throughout notebook" ] }, { @@ -113,6 +77,7 @@ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from L96_model import L96, RK4, L96_2t_xdot_ydot, L96_eq1_xdot, L96s\n", + "import DA_methods\n", "\n", "rng = np.random.default_rng()" ] @@ -140,7 +105,7 @@ " dt = 0.005 # Model timestep\n", " si = 0.005 # Truth sampling interval\n", " seasonal = False # Option for adding a seasonal cycle to the forcing in the L96 truth model\n", - " B_loc = 5 # Spatial localization radius for DA\n", + " B_loc = 5 # Spatial localization radius for DA in terms of model grid points\n", " DA = \"EnKF\" # DA method\n", " nens = 500 # Number of ensemble members for DA\n", " inflate_opt = \"relaxation\" # Method for DA model covariance inflation\n", @@ -158,34 +123,6 @@ " # fmt: on" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "3824759d-3678-4915-9793-55595d0989e8", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def observation_operator(K, l_obs, t_obs, i_t):\n", - " \"\"\"Observation operator to map between model and observation space,\n", - " assuming linearity and model space observations.\n", - "\n", - " Args:\n", - " K: spatial dimension of the model\n", - " l_obs: spatial positions of observations on model grid\n", - " t_obs: time positions of observations\n", - " i_t: the timestep of the current DA cycle\n", - "\n", - " Returns:\n", - " Operator matrix (K * observation_density, K)\n", - " \"\"\"\n", - " n = l_obs.shape[-1]\n", - " H = np.zeros((n, K))\n", - " H[range(n), l_obs[t_obs == i_t]] = 1\n", - " return H" - ] - }, { "cell_type": "code", "execution_count": null, @@ -224,156 +161,6 @@ " return hist, time" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "4e65b0ea-ba54-406e-878c-39b46e776022", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def get_dist(i, j, K):\n", - " \"\"\"Compute the absolute distance between two element indices\n", - " within a square matrix of size (K x K)\n", - "\n", - " Args:\n", - " i: the ith row index\n", - " j: the jth column index\n", - " K: shape of square array\n", - "\n", - " Returns:\n", - " Distance\n", - " \"\"\"\n", - " return abs(i - j) if abs(i - j) <= K / 2 else K - abs(i - j)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5ab2c12b-3b13-4557-9228-60222de7470c", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def gaspari_cohn(distance, radius):\n", - " \"\"\"Compute the appropriate distance dependent weighting of a\n", - " covariance matrix, after Gaspari & Cohn, 1999 (https://doi.org/10.1002/qj.49712555417)\n", - "\n", - " Args:\n", - " distance: the distance between array elements\n", - " radius: localization radius for DA\n", - "\n", - " Returns:\n", - " distance dependent weight of the (i,j) index of a covariance matrix\n", - " \"\"\"\n", - " if distance == 0:\n", - " weight = 1.0\n", - " else:\n", - " if radius == 0:\n", - " weight = 0.0\n", - " else:\n", - " ratio = distance / radius\n", - " weight = 0.0\n", - " if ratio <= 1:\n", - " weight = (\n", - " -(ratio**5) / 4\n", - " + ratio**4 / 2\n", - " + 5 * ratio**3 / 8\n", - " - 5 * ratio**2 / 3\n", - " + 1\n", - " )\n", - " elif ratio <= 2:\n", - " weight = (\n", - " ratio**5 / 12\n", - " - ratio**4 / 2\n", - " + 5 * ratio**3 / 8\n", - " + 5 * ratio**2 / 3\n", - " - 5 * ratio\n", - " + 4\n", - " - 2 / 3 / ratio\n", - " )\n", - " return weight" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "86f93dee-eea4-44e0-9ad6-113ab0912688", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def localize_covariance(B, loc=0):\n", - " \"\"\"Localize the model climatology covariance matrix, based on\n", - " the Gaspari-Cohn function.\n", - "\n", - " Args:\n", - " B: Covariance matrix over a long model run 'M_truth' (K, K)\n", - " loc: spatial localization radius for DA\n", - "\n", - " Returns:\n", - " Covariance matrix scaled to zero outside distance 'loc' from diagonal and\n", - " the matrix of weights which are used to scale covariance matrix\n", - " \"\"\"\n", - " M, N = B.shape\n", - " X, Y = np.ix_(np.arange(M), np.arange(N))\n", - " dist = np.vectorize(get_dist)(X, Y, M)\n", - " W = np.vectorize(gaspari_cohn)(dist, loc)\n", - " return B * W, W" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "fc3b629d-398b-4b96-9d63-e95eaab8f688", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def running_average(X, N):\n", - " \"\"\"Compute running mean over a user-specified window.\n", - "\n", - " Args:\n", - " X: Input vector of arbitrary length 'n'\n", - " N: Size of window over which to compute mean\n", - "\n", - " Returns:\n", - " X averaged over window N\n", - " \"\"\"\n", - " if N % 2 == 0:\n", - " N1, N2 = -N / 2, N / 2\n", - " else:\n", - " N1, N2 = -(N - 1) / 2, (N + 1) / 2\n", - " X_sum = np.zeros(X.shape)\n", - " for i in np.arange(N1, N2):\n", - " X_sum = X_sum + np.roll(X, int(i), axis=0)\n", - " return X_sum / N" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "e6a648d4-d5af-419c-bdaa-9dd81b14cffe", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def find_obs(loc, obs, t_obs, l_obs, period):\n", - " \"\"\"NOTE: This function is for plotting purposes only.\"\"\"\n", - " t_period = np.where((t_obs[:, 0] >= period[0]) & (t_obs[:, 0] < period[1]))\n", - " obs_period = np.zeros(t_period[0].shape)\n", - " obs_period[:] = np.nan\n", - " for i in np.arange(len(obs_period)):\n", - " if np.any(l_obs[t_period[0][i]] == loc):\n", - " obs_period[i] = obs[t_period[0][i]][l_obs[t_period[0][i]] == loc]\n", - " return obs_period" - ] - }, { "cell_type": "markdown", "id": "6d3052af", @@ -495,7 +282,7 @@ "user_expressions": [] }, "source": [ - "Now, we generate climatological background (temporal) covariance for the 2-scale L96 model" + "Now, we generate climatological background (temporal) covariance `B_clim2` for the 2-scale L96 model." ] }, { @@ -572,7 +359,7 @@ "user_expressions": [] }, "source": [ - "Generating climatological background covariance for 1-scale L96 model" + "Generating climatological background covariance `B_clim1` for 1-scale L96 model. This climatological covariance will be used by the 3-dimensional variational (3DVar) DA method, or by the hybrid 3DVar-EnKF method. Since we cannot observe every state variable at every possible location, when assimilting sparse observations into the model, we need to use each observation to update multiple model locations, usually around the observed location. The covariance are thus needed to project the model-observation misfits between different model locations in certain DA methods such as 3DVar and EnKF." ] }, { @@ -599,7 +386,7 @@ "source": [ "# 3. Generate synthetic observations\n", "\n", - "Here we generate a set of sparse observations by sampling from the `X_truth` run and adding some random Gaussian noise." + "Here we generate a set of sparse observations by sampling from the `X_truth` run and adding some random Gaussian noise. The observations are stored as individual samples, each containing the time, location, and value." ] }, { @@ -633,7 +420,7 @@ "user_expressions": [] }, "source": [ - "The covariance matrix over the observations `R` (used to express the uncertainty in the observations during DA) is given as a diagonal matrix with entries defined by the square of the \"observational error standard deviation\"." + "The covariance matrix `R` for the observations (used to express the uncertainty in the observations during DA) is given as a diagonal matrix with entries defined by the square of the \"observational error standard deviation\". $R$ is a diagonal matrix because we assume that the errors of different observations are independent. The function `find_obs` is used here to find the locations and values of a set of observations given the observed times. " ] }, { @@ -662,7 +449,7 @@ "plt.plot(range(1000, 1500), X_truth[1000:1500, 0], label=\"truth\")\n", "plt.scatter(\n", " t_obs[100:150, 0],\n", - " find_obs(0, X_obs, t_obs, l_obs, [t_obs[100, 0], t_obs[150, 0]]),\n", + " DA_methods.find_obs(0, X_obs, t_obs, l_obs, [t_obs[100, 0], t_obs[150, 0]]),\n", " color=\"k\",\n", " label=\"obs\",\n", ")\n", @@ -676,36 +463,9 @@ "user_expressions": [] }, "source": [ - "# 4. Apply Localization to the Background Model Covariance\n", - "\n", - "The covariance of the model climatology was computed a-priori from a long run. In this step we apply the localized weighting to the covariance matrix." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5f5501b8-82d7-428a-a030-47d8c50fc4bb", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import importlib\n", - "\n", - "import DA_methods\n", + "# 4. Check the Model Background Covariances for the variable `X`\n", "\n", - "importlib.reload(DA_methods);" - ] - }, - { - "cell_type": "markdown", - "id": "eb095211-2a3f-47c1-899c-ecd4bc4a802d", - "metadata": { - "tags": [], - "user_expressions": [] - }, - "source": [ - "Load pre-calculated climatological background covariance matrix from a long simulation" + "The climatological covariances of both the \"truth\" (2-scale L96) and \"GCM\" (1-scale L96) are computed a-priori from a long run. " ] }, { @@ -717,8 +477,6 @@ }, "outputs": [], "source": [ - "B_loc, W_clim = localize_covariance(B_clim1, loc=Config.B_loc)\n", - "\n", "B_corr1 = np.zeros(B_clim1.shape)\n", "B_corr2 = np.zeros(B_clim2.shape)\n", "for i in range(B_clim1.shape[0]):\n", @@ -810,6 +568,11 @@ }, "outputs": [], "source": [ + "# Localize the covariance matrix in advance to avoid the calculation at each DA step\n", + "# The localization weight matrix is also saved for EnKF\n", + "\n", + "B_loc, W_clim = DA_methods.localize_covariance(B_clim1, loc=Config.B_loc)\n", + "\n", "if Config.param_DA:\n", " mean_param = np.zeros((int(Config.ns_da / Config.DA_freq), len(Config.GCM_param)))\n", " spread_param = np.zeros((int(Config.ns_da / Config.DA_freq), len(Config.GCM_param)))\n", @@ -868,7 +631,7 @@ " # Call DA\n", " t_DA[cycle] = t_truth[i_t]\n", " if Config.DA == \"EnKF\":\n", - " H = observation_operator(Config.K, l_obs, t_obs, i_t)\n", + " H = DA_methods.observation_operator(Config.K, l_obs, t_obs, i_t)\n", "\n", " # Augment state vector with parameters when doing parameter estimation\n", " if Config.param_DA:\n", @@ -897,7 +660,7 @@ " ens_param = X_post[-len(Config.GCM_param) :, :]\n", "\n", " elif Config.DA == \"HyEnKF\":\n", - " H = observation_operator(Config.K, l_obs, t_obs, i_t)\n", + " H = DA_methods.observation_operator(Config.K, l_obs, t_obs, i_t)\n", " B_ens = (\n", " np.cov(X_prior) * (1 - Config.hybrid_factor)\n", " + B_clim1 * Config.hybrid_factor\n", @@ -910,7 +673,7 @@ "\n", " elif Config.DA == \"3DVar\":\n", " X_prior = np.squeeze(X_prior)\n", - " H = observation_operator(Config.K, l_obs, t_obs, i_t)\n", + " H = DA_methods.observation_operator(Config.K, l_obs, t_obs, i_t)\n", " X_post = DA_methods.Lin3dvar(X_prior, X_obs[t_obs == i_t], H, R, B_loc, 3)\n", "\n", " elif Config.DA == \"Replace\":\n", @@ -1014,7 +777,7 @@ "X_inc_ave = X_inc / Config.DA_freq / Config.si\n", "axes[0, 2].plot(M_truth.k, X_inc_ave.mean(axis=(0, -1)), label=\"Inc\")\n", "axes[0, 2].plot(\n", - " M_truth.k, running_average(X_inc_ave.mean(axis=(0, -1)), 7), label=\"Inc Ave\"\n", + " M_truth.k, DA_methods.running_average(X_inc_ave.mean(axis=(0, -1)), 7), label=\"Inc Ave\"\n", ")\n", "axes[0, 2].plot(\n", " M_truth.k,\n", @@ -1046,7 +809,7 @@ ")\n", "axes[1, 0].scatter(\n", " t_DA[plot_start_DA - 1 : plot_end_DA - 1],\n", - " find_obs(plot_x, X_obs, t_obs, l_obs, [plot_start, plot_end]),\n", + " DA_methods.find_obs(plot_x, X_obs, t_obs, l_obs, [plot_start, plot_end]),\n", " label=\"obs\",\n", ")\n", "axes[1, 0].grid(which=\"both\", linestyle=\"--\")\n", @@ -1058,7 +821,7 @@ " for i, c in zip(np.arange(len(Config.GCM_param), 0, -1), [\"r\", \"b\", \"g\", \"k\"]):\n", " axes[1, 1].plot(\n", " t_DA,\n", - " running_average(mean_param[:, i - 1], 100),\n", + " DA_methods.running_average(mean_param[:, i - 1], 100),\n", " c + \"-\",\n", " label=\"C{} {:3f}\".format(\n", " i - 1, mean_param[int(len(t_DA) / 2) :, i - 1].mean()\n", @@ -1066,13 +829,13 @@ " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " running_average(mean_param[:, i - 1] + spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(mean_param[:, i - 1] + spread_param[:, i - 1], 100),\n", " c + \":\",\n", " label=f\"SD {spread_param[int(len(t_DA) / 2):, i - 1].mean():3f}\",\n", " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " running_average(mean_param[:, i - 1] - spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(mean_param[:, i - 1] - spread_param[:, i - 1], 100),\n", " c + \":\",\n", " )\n", " axes[1, 1].legend()\n", diff --git a/notebooks/DA_methods.py b/notebooks/DA_methods.py index e35faba5..edc6c714 100644 --- a/notebooks/DA_methods.py +++ b/notebooks/DA_methods.py @@ -1,10 +1,127 @@ """ Data assimilation methods -Adapted form PyDA project: https://github.com/Shady-Ahmed/PyDA +Partly adapted form PyDA project: https://github.com/Shady-Ahmed/PyDA Reference: https://www.mdpi.com/2311-5521/5/4/225 """ import numpy as np from numba import njit +def observation_operator(K, l_obs, t_obs, i_t): + """Observation operator to map between model and observation space, + assuming linearity and model space observations. + + Args: + K: spatial dimension of the model + l_obs: spatial positions of observations on model grid + t_obs: time positions of observations + i_t: the timestep of the current DA cycle + + Returns: + Operator matrix (K * observation_density, K) + """ + n = l_obs.shape[-1] + H = np.zeros((n, K)) + H[range(n), l_obs[t_obs == i_t]] = 1 + return H + +def get_dist(i, j, K): + """Compute the absolute distance between two element indices + within a square matrix of size (K x K) + + Args: + i: the ith row index + j: the jth column index + K: shape of square array + + Returns: + Distance + """ + return abs(i - j) if abs(i - j) <= K / 2 else K - abs(i - j) + +def gaspari_cohn(distance, radius): + """Compute the appropriate distance dependent weighting of a + covariance matrix, after Gaspari & Cohn, 1999 (https://doi.org/10.1002/qj.49712555417) + + Args: + distance: the distance between array elements + radius: localization radius for DA + + Returns: + distance dependent weight of the (i,j) index of a covariance matrix + """ + if distance == 0: + weight = 1.0 + else: + if radius == 0: + weight = 0.0 + else: + ratio = distance / radius + weight = 0.0 + if ratio <= 1: + weight = ( + -(ratio**5) / 4 + + ratio**4 / 2 + + 5 * ratio**3 / 8 + - 5 * ratio**2 / 3 + + 1 + ) + elif ratio <= 2: + weight = ( + ratio**5 / 12 + - ratio**4 / 2 + + 5 * ratio**3 / 8 + + 5 * ratio**2 / 3 + - 5 * ratio + + 4 + - 2 / 3 / ratio + ) + return weight + +def localize_covariance(B, loc=0): + """Localize the model climatology covariance matrix, based on + the Gaspari-Cohn function. + + Args: + B: Covariance matrix over a long model run 'M_truth' (K, K) + loc: spatial localization radius for DA + + Returns: + Covariance matrix scaled to zero outside distance 'loc' from diagonal and + the matrix of weights which are used to scale covariance matrix + """ + M, N = B.shape + X, Y = np.ix_(np.arange(M), np.arange(N)) + dist = np.vectorize(get_dist)(X, Y, M) + W = np.vectorize(gaspari_cohn)(dist, loc) + return B * W, W + +def running_average(X, N): + """Compute running mean over a user-specified window. + + Args: + X: Input vector of arbitrary length 'n' + N: Size of window over which to compute mean + + Returns: + X averaged over window N + """ + if N % 2 == 0: + N1, N2 = -N / 2, N / 2 + else: + N1, N2 = -(N - 1) / 2, (N + 1) / 2 + X_sum = np.zeros(X.shape) + for i in np.arange(N1, N2): + X_sum = X_sum + np.roll(X, int(i), axis=0) + return X_sum / N + +def find_obs(loc, obs, t_obs, l_obs, period): + """NOTE: This function is for plotting purposes only.""" + t_period = np.where((t_obs[:, 0] >= period[0]) & (t_obs[:, 0] < period[1])) + obs_period = np.zeros(t_period[0].shape) + obs_period[:] = np.nan + for i in np.arange(len(obs_period)): + if np.any(l_obs[t_period[0][i]] == loc): + obs_period[i] = obs[t_period[0][i]][l_obs[t_period[0][i]] == loc] + return obs_period @njit def Lin3dvar(ub, w, H, R, B, opt): From 3ec9e1e5190bf6ed1295054388b9fba7c33afced Mon Sep 17 00:00:00 2001 From: Feiyu Lu Date: Wed, 19 Jul 2023 16:32:28 -0400 Subject: [PATCH 03/10] Reorganized the DA steps --- notebooks/DA_demo_L96.ipynb | 14 +++----------- 1 file changed, 3 insertions(+), 11 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index cfaf1a9b..8547f3b6 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -39,10 +39,10 @@ "We use the 2-scale Lorenz-96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". Detailed description of this setup can be find here (https://m2lines.github.io/L96_demo/notebooks/gcm-analogue.html). This is what we call an idealized biased-model framework in DA research, in the sense that our DA model is biased compared to the truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", "\n", "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", - "1. Generate a “truth” signal from 2-scale L96 model\n", - "2. Specify a biased “GCM”model for performing DA\n", + "1. Specify a biased “GCM”model for performing DA\n", " * Choose P (to start, use GCM with P=0).\n", " * Choose F_GCM (to start, use F_GCM=F).\n", + "2. Generate a “truth” signal from 2-scale L96 model\n", "3. Collect sparse and noisy observations, sampled from “truth”\n", " * Specify observation density in space, frequency in time\n", " * Specify observational error\n", @@ -463,7 +463,7 @@ "user_expressions": [] }, "source": [ - "# 4. Check the Model Background Covariances for the variable `X`\n", + "# Check the Model Background Covariances for the variable `X`\n", "\n", "The climatological covariances of both the \"truth\" (2-scale L96) and \"GCM\" (1-scale L96) are computed a-priori from a long run. " ] @@ -923,14 +923,6 @@ " X_inc_ave=X_inc_ave,\n", " )" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1e96ab6d-95db-4882-ab8c-687b0f9c68bd", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From 4f420e4326f4c94b403940fb77a2149cf5bb6420 Mon Sep 17 00:00:00 2001 From: Feiyu Lu Date: Wed, 19 Jul 2023 16:33:13 -0400 Subject: [PATCH 04/10] Reorganized the DA steps --- notebooks/DA_demo_L96.ipynb | 100 ++++++++++++++++-------------------- 1 file changed, 44 insertions(+), 56 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index cfaf1a9b..8dd81f90 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -39,16 +39,14 @@ "We use the 2-scale Lorenz-96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". Detailed description of this setup can be find here (https://m2lines.github.io/L96_demo/notebooks/gcm-analogue.html). This is what we call an idealized biased-model framework in DA research, in the sense that our DA model is biased compared to the truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", "\n", "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", - "1. Generate a “truth” signal from 2-scale L96 model\n", - "2. Specify a biased “GCM”model for performing DA\n", - " * Choose P (to start, use GCM with P=0).\n", - " * Choose F_GCM (to start, use F_GCM=F).\n", + "1. Specify a biased “GCM” model for performing DA, and set the parameters for the \"GCM\", observations, and DA method in `Config`.\n", + " * Parameters to experiment in `Config`: forcing `F`, seasonal cycle, experiment length, \n", + "2. Generate a “truth” signal from the 2-scale L96 model\n", "3. Collect sparse and noisy observations, sampled from “truth”\n", - " * Specify observation density in space, frequency in time\n", - " * Specify observational error\n", + " * Parameters to experiment in `Config`: observation density in space, frequency in time, observational error\n", "4. Perform DA using a method of choice\n", - " * Choose DA method: EnKF, 3DVAR, Hybrid EnKF\n", - " * Specify DA setup: ensemble members, localization, inflation\n", + " * Parameters to experiment in `Config`: DA method (EnKF, 3DVAR, Hybrid EnKF), DA frequency, ensemble size (for EnKF), localization, inflation method and factor\n", + " * Optional: parameter estimation to recover the true forcing\n", "5. Assess DA performance\n", " * RMSE of DA experiment relative to truth\n", "6. Analyze DA increments to assess GCM model error (optional)\n" @@ -85,11 +83,47 @@ { "cell_type": "code", "execution_count": null, - "id": "e2c3e7af", + "id": "ebf223e6-ed8a-425a-b808-55b0cc59c69c", "metadata": { "tags": [] }, "outputs": [], + "source": [ + "def GCM(X_init, F, dt, nt, param=[0]):\n", + " \"\"\"A toy `General Circulation Model` (GCM) that uses the single time-scale Lorenz 1996 model\n", + " with a parameterised coupling term to represent the interaction between the observed coarse\n", + " scale processes `X` and unobserved fine scale processes `Y` of the two time-scale model.\n", + "\n", + " Args:\n", + " X_init: Initial conditions of X\n", + " F: Forcing term\n", + " dt: Sampling frequency of the model\n", + " nt: Number of timesteps for which to run the model\n", + " param: Weights to give to the coupling term\n", + "\n", + " Returns:\n", + " Model output for all variables of X at each timestep along with the corresponding time units\n", + " \"\"\"\n", + " time, hist, X = (\n", + " dt * np.arange(nt + 1),\n", + " np.zeros((nt + 1, len(X_init))) * np.nan,\n", + " X_init.copy(),\n", + " )\n", + " hist[0] = X\n", + "\n", + " for n in range(nt):\n", + " X = X + dt * (L96_eq1_xdot(X, F) - np.polyval(param, X))\n", + " hist[n + 1], time[n + 1] = X, dt * (n + 1)\n", + "\n", + " return hist, time" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3d2efdbe", + "metadata": {}, + "outputs": [], "source": [ "class Config:\n", " # fmt: off\n", @@ -123,44 +157,6 @@ " # fmt: on" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "ebf223e6-ed8a-425a-b808-55b0cc59c69c", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def GCM(X_init, F, dt, nt, param=[0]):\n", - " \"\"\"A toy `General Circulation Model` (GCM) that uses the single time-scale Lorenz 1996 model\n", - " with a parameterised coupling term to represent the interaction between the observed coarse\n", - " scale processes `X` and unobserved fine scale processes `Y` of the two time-scale model.\n", - "\n", - " Args:\n", - " X_init: Initial conditions of X\n", - " F: Forcing term\n", - " dt: Sampling frequency of the model\n", - " nt: Number of timesteps for which to run the model\n", - " param: Weights to give to the coupling term\n", - "\n", - " Returns:\n", - " Model output for all variables of X at each timestep along with the corresponding time units\n", - " \"\"\"\n", - " time, hist, X = (\n", - " dt * np.arange(nt + 1),\n", - " np.zeros((nt + 1, len(X_init))) * np.nan,\n", - " X_init.copy(),\n", - " )\n", - " hist[0] = X\n", - "\n", - " for n in range(nt):\n", - " X = X + dt * (L96_eq1_xdot(X, F) - np.polyval(param, X))\n", - " hist[n + 1], time[n + 1] = X, dt * (n + 1)\n", - "\n", - " return hist, time" - ] - }, { "cell_type": "markdown", "id": "6d3052af", @@ -463,7 +459,7 @@ "user_expressions": [] }, "source": [ - "# 4. Check the Model Background Covariances for the variable `X`\n", + "# Check the Model Background Covariances for the variable `X`\n", "\n", "The climatological covariances of both the \"truth\" (2-scale L96) and \"GCM\" (1-scale L96) are computed a-priori from a long run. " ] @@ -923,14 +919,6 @@ " X_inc_ave=X_inc_ave,\n", " )" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1e96ab6d-95db-4882-ab8c-687b0f9c68bd", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From 19c8fc6c86ae38eb07fd207433cad0bba82b8d5e Mon Sep 17 00:00:00 2001 From: Feiyu Lu Date: Wed, 19 Jul 2023 16:36:16 -0400 Subject: [PATCH 05/10] Fixed conflicts --- notebooks/DA_demo_L96.ipynb | 7 ------- 1 file changed, 7 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 03ffc4fc..8dd81f90 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -39,16 +39,9 @@ "We use the 2-scale Lorenz-96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". Detailed description of this setup can be find here (https://m2lines.github.io/L96_demo/notebooks/gcm-analogue.html). This is what we call an idealized biased-model framework in DA research, in the sense that our DA model is biased compared to the truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", "\n", "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", -<<<<<<< HEAD "1. Specify a biased “GCM” model for performing DA, and set the parameters for the \"GCM\", observations, and DA method in `Config`.\n", " * Parameters to experiment in `Config`: forcing `F`, seasonal cycle, experiment length, \n", "2. Generate a “truth” signal from the 2-scale L96 model\n", -======= - "1. Specify a biased “GCM”model for performing DA\n", - " * Choose P (to start, use GCM with P=0).\n", - " * Choose F_GCM (to start, use F_GCM=F).\n", - "2. Generate a “truth” signal from 2-scale L96 model\n", ->>>>>>> 3ec9e1e5190bf6ed1295054388b9fba7c33afced "3. Collect sparse and noisy observations, sampled from “truth”\n", " * Parameters to experiment in `Config`: observation density in space, frequency in time, observational error\n", "4. Perform DA using a method of choice\n", From e3f507e3be0212202070be5882df39d873f559c6 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Wed, 2 Aug 2023 18:05:40 +0000 Subject: [PATCH 06/10] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- notebooks/DA_demo_L96.ipynb | 12 +- notebooks/DA_methods.py | 7 + notebooks/gradient_decent.ipynb | 42 +- .../old_notebooks/gradient_decent-old.ipynb | 1485 +---------------- 4 files changed, 64 insertions(+), 1482 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 8dd81f90..d35ba368 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -773,7 +773,9 @@ "X_inc_ave = X_inc / Config.DA_freq / Config.si\n", "axes[0, 2].plot(M_truth.k, X_inc_ave.mean(axis=(0, -1)), label=\"Inc\")\n", "axes[0, 2].plot(\n", - " M_truth.k, DA_methods.running_average(X_inc_ave.mean(axis=(0, -1)), 7), label=\"Inc Ave\"\n", + " M_truth.k,\n", + " DA_methods.running_average(X_inc_ave.mean(axis=(0, -1)), 7),\n", + " label=\"Inc Ave\",\n", ")\n", "axes[0, 2].plot(\n", " M_truth.k,\n", @@ -825,13 +827,17 @@ " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " DA_methods.running_average(mean_param[:, i - 1] + spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(\n", + " mean_param[:, i - 1] + spread_param[:, i - 1], 100\n", + " ),\n", " c + \":\",\n", " label=f\"SD {spread_param[int(len(t_DA) / 2):, i - 1].mean():3f}\",\n", " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " DA_methods.running_average(mean_param[:, i - 1] - spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(\n", + " mean_param[:, i - 1] - spread_param[:, i - 1], 100\n", + " ),\n", " c + \":\",\n", " )\n", " axes[1, 1].legend()\n", diff --git a/notebooks/DA_methods.py b/notebooks/DA_methods.py index edc6c714..6f49fe10 100644 --- a/notebooks/DA_methods.py +++ b/notebooks/DA_methods.py @@ -5,6 +5,7 @@ import numpy as np from numba import njit + def observation_operator(K, l_obs, t_obs, i_t): """Observation operator to map between model and observation space, assuming linearity and model space observations. @@ -23,6 +24,7 @@ def observation_operator(K, l_obs, t_obs, i_t): H[range(n), l_obs[t_obs == i_t]] = 1 return H + def get_dist(i, j, K): """Compute the absolute distance between two element indices within a square matrix of size (K x K) @@ -37,6 +39,7 @@ def get_dist(i, j, K): """ return abs(i - j) if abs(i - j) <= K / 2 else K - abs(i - j) + def gaspari_cohn(distance, radius): """Compute the appropriate distance dependent weighting of a covariance matrix, after Gaspari & Cohn, 1999 (https://doi.org/10.1002/qj.49712555417) @@ -76,6 +79,7 @@ def gaspari_cohn(distance, radius): ) return weight + def localize_covariance(B, loc=0): """Localize the model climatology covariance matrix, based on the Gaspari-Cohn function. @@ -94,6 +98,7 @@ def localize_covariance(B, loc=0): W = np.vectorize(gaspari_cohn)(dist, loc) return B * W, W + def running_average(X, N): """Compute running mean over a user-specified window. @@ -113,6 +118,7 @@ def running_average(X, N): X_sum = X_sum + np.roll(X, int(i), axis=0) return X_sum / N + def find_obs(loc, obs, t_obs, l_obs, period): """NOTE: This function is for plotting purposes only.""" t_period = np.where((t_obs[:, 0] >= period[0]) & (t_obs[:, 0] < period[1])) @@ -123,6 +129,7 @@ def find_obs(loc, obs, t_obs, l_obs, period): obs_period[i] = obs[t_period[0][i]][l_obs[t_period[0][i]] == loc] return obs_period + @njit def Lin3dvar(ub, w, H, R, B, opt): # The solution of the 3DVAR problem in the linear case requires diff --git a/notebooks/gradient_decent.ipynb b/notebooks/gradient_decent.ipynb index 1440ecd3..2be456c6 100644 --- a/notebooks/gradient_decent.ipynb +++ b/notebooks/gradient_decent.ipynb @@ -200,7 +200,7 @@ "metadata": {}, "outputs": [], "source": [ - "# We create 100 data points. \n", + "# We create 100 data points.\n", "n = 100\n", "x = torch.ones(n, 2)\n", "\n", @@ -287,7 +287,7 @@ "metadata": {}, "outputs": [], "source": [ - "# Initialize parameters with some randomly guessed values. \n", + "# Initialize parameters with some randomly guessed values.\n", "w_real = torch.as_tensor([-3.0, -5])\n", "y_hat = x @ w_real\n", "# Initial mean-squared error\n", @@ -311,7 +311,7 @@ "plt.scatter(x[:, 1], y, label=\"y\")\n", "plt.scatter(x[:, 1], y_hat, label=\"$\\\\tilde{y}$\")\n", "plt.xlabel(\"$x$\")\n", - "plt.title('Prediction of model using non-optimized model')\n", + "plt.title(\"Prediction of model using non-optimized model\")\n", "plt.legend(fontsize=7);" ] }, @@ -451,7 +451,7 @@ "plt.plot(np.array(losses))\n", "plt.xlabel(\"Iteration\")\n", "plt.ylabel(\"Loss\")\n", - "plt.yscale('log')\n", + "plt.yscale(\"log\")\n", "plt.title(\"Loss vs Iteration\")\n", "plt.show();" ] @@ -547,13 +547,13 @@ "source": [ "# We create many data points, as neural networks need lot of data to train from scratch.\n", "n = 10000\n", - "x = torch.ones(n,1)\n", + "x = torch.ones(n, 1)\n", "\n", "# uniformly sample x points between -1 and 1.\n", "# Underscore functions in pytorch means replace the value (update)\n", "x = x.uniform_(-1.0, 1)\n", "\n", - "y = torch.sin(x* 2*torch.pi) + 0.1*torch.rand(n, 1) " + "y = torch.sin(x * 2 * torch.pi) + 0.1 * torch.rand(n, 1)" ] }, { @@ -569,7 +569,7 @@ "metadata": {}, "outputs": [], "source": [ - "plt.plot(x[:,0], y, '.', markersize=0.5)" + "plt.plot(x[:, 0], y, \".\", markersize=0.5)" ] }, { @@ -592,12 +592,12 @@ "class Simple_Neural_Net(nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", - " self.Dense1 = nn.Linear(1, 30) \n", - " self.Dense2 = nn.Linear(30,30)\n", - " self.Dense3 = nn.Linear(30,1)\n", - " \n", + " self.Dense1 = nn.Linear(1, 30)\n", + " self.Dense2 = nn.Linear(30, 30)\n", + " self.Dense3 = nn.Linear(30, 1)\n", + "\n", " self.relu = nn.ReLU()\n", - " \n", + "\n", " def forward(self, x):\n", " # This method is automatically executed when\n", " # we call a object of this class\n", @@ -627,7 +627,9 @@ "source": [ "net_input = torch.randn(1, 1)\n", "out = neural_net(net_input)\n", - "print(f\"The output of the random input {net_input.item():.4f} from untrained network is: {out.item():.4f}\")" + "print(\n", + " f\"The output of the random input {net_input.item():.4f} from untrained network is: {out.item():.4f}\"\n", + ")" ] }, { @@ -689,7 +691,6 @@ "outputs": [], "source": [ "def train_step(model, loss_fn, optimizer):\n", - " \n", " # Set the model to training mode - important for batch normalization and dropout layers\n", " # Unnecessary in this situation but added for best practices\n", "\n", @@ -725,8 +726,7 @@ "for t in range(epochs):\n", " Loss[t] = train_step(neural_net, loss_fn, optimizer)\n", " if np.mod(t, 200) == 0:\n", - " print(f\"Loss at Epoch {t+1} is \", Loss[t])\n", - " " + " print(f\"Loss at Epoch {t+1} is \", Loss[t])" ] }, { @@ -739,7 +739,7 @@ "plt.plot(Loss)\n", "plt.xlabel(\"Iteration\")\n", "plt.ylabel(\"Loss\")\n", - "plt.yscale('log')\n", + "plt.yscale(\"log\")\n", "plt.title(\"Loss vs Iteration\")\n", "plt.show();" ] @@ -761,8 +761,8 @@ "source": [ "# Generate some points where the predictions of the model will be tested.\n", "# Here we pick the testing domain to be larger than the training domain to check if the model\n", - "# has any skill at extrapolation. \n", - "x_test = torch.linspace(-1.5, 1.5, 501).reshape(501,1)\n", + "# has any skill at extrapolation.\n", + "x_test = torch.linspace(-1.5, 1.5, 501).reshape(501, 1)\n", "\n", "# Generate the predictions from the trained model.\n", "pred = neural_net(x_test).detach().numpy()" @@ -776,8 +776,8 @@ "source": [ "plt.figure(dpi=150)\n", "\n", - "plt.plot(x, y, '.', markersize=0.5, label='Data')\n", - "plt.plot(x_test, pred, markersize=0.5, label='Predicted fit')\n", + "plt.plot(x, y, \".\", markersize=0.5, label=\"Data\")\n", + "plt.plot(x_test, pred, markersize=0.5, label=\"Predicted fit\")\n", "\n", "plt.legend()" ] diff --git a/notebooks/old_notebooks/gradient_decent-old.ipynb b/notebooks/old_notebooks/gradient_decent-old.ipynb index 94c3ce82..cbed645a 100644 --- a/notebooks/old_notebooks/gradient_decent-old.ipynb +++ b/notebooks/old_notebooks/gradient_decent-old.ipynb @@ -116,7 +116,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -144,7 +144,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -160,20 +160,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "tensor([3., 2.])" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "w = torch.as_tensor([3.0, 2])\n", "w" @@ -200,24 +189,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "tensor([[ 1.0000, 0.2203],\n", - " [ 1.0000, -0.1899],\n", - " [ 1.0000, 0.7698],\n", - " [ 1.0000, 0.3822],\n", - " [ 1.0000, -0.2894]])" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "n = 100\n", "x = torch.ones(n, 2)\n", @@ -229,7 +203,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -238,20 +212,9 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Ub/PklC4zkr0eR9va3pt1wcfz5ayPFg6HtXnzZknSxz72sQz3BgAAwH3iIyfrGhOPFsRHTpavaVQkGktzD4fb3R9RXUu3qTZ1LV0K9w861CN3GBgcu6CBne28zJPBZ+vWrXrhhRd09PKkN954Q1dddZX27dunyy+/XNOnm9vcCgAAIBtYGTnJtFSmdPlZXo61CVxW23mZJ4PP9u3b9YlPfEKnnHKKFi1apL/927/Vxz/+cX3kIx/RSy+9pJKSEv30pz/NdDcBAABcx6sjJ6lM6fKzZDdyPdrCGZNs7on7eTL4lJeX64YbbtDUqVO1bds2Pfroo3r99df10Y9+VPfcc4+ampp00kknZbqbAAAAruPVkROmdI2sakGhQsGAqTahYEBV8wsd6pF7eXKM6yMf+YgefPDBTHcDAADAc7y6GJ4pXSM7KT9XlaXTTe3jU1nqvop96eDJER8AAABY49WRE6Z0JVZdUZL09SkvLlB1xVyHe+ROBB8AAIAs4tWRE6Z0JZYbCmrtijItKytKeI1CwYCWlRVlxd5Gifh77A8AAMBF3LBZaHlxgTa39Zhul+mRE6Z0jS43FNSqpfO0csls1TZ3aWt7r+s3pE23gHF0TWhIkkpKSiRJra2tGe4JAADwutE2C5UO/TY+XZuF7u6P6LzVz5sqcBAKBrTltosy/uAc338omXVK5cUFWT264UepPp8z1Q0AAMBBbtssND5yYoZbRk6Y0oVUMOKTACM+AADADrdveNXU9KxlZUVatXSegz3yx8hJuH+QKV1ZJtXnc4JPAgQfAACQKjdPKzs0/W6b6lpGHolK5/Q7IBmpPp9T3AAAAMAhqWwW6vSeOV5ZDO+GghDwB4IPAACAQ7ywWeiU/BzdtHhWRjcnHcloBSE2t/Xovo07GZGCKQQfAAAAh3h1s9BMS2YNUrwgRHt4IOEaJEaLcCSCDwAAgEO8ulloptXUtyY9WtbQ0aea+m1DCkIwWoSRUM4aAADAIeXFBZbaZXqz0Eza3R9RXUu3qTZ1LV0K9w9Kcl/5cLgHwQcAAMAhVQsKE+43k0goGFDV/EKHeuR+qRSEkKyNFiE7EHwAAAAc4uXNQjMllYIQqY4Wwd8IPgAAAA6qrihJespbeXGBqivmOtwjd0ulIESqo0XwN4IPAACAg3JDQa1dUaZlZUUJp72FggEtKytKWJ0sm6RSECKV0SL4X3aXDAEAAFkvHSWPvbJZqBuUFxdoc1uP6XYLZ0zSxj++a+mc2V4+PFsQfAAAQFbKRMljt24W6iZVCwp1/6Y2U1PW4gUhrI7cZHv58GzBVDcAAJB1KHnsXqkUhLBaPrz01BMttYO3EHwAAEDWoeSxOeH+Qf3w+TZd+1CDrnrwJV37UIN+9MKfHKuGZrUghJXy4ZL0u51hwm0WIPgAAICsQsnj5EWiMd2+4VWdu3qT7n52pza39eiVzj3a3Naju57ZoXNXb9LtG16zPTRYLQhhZbRIkl7u3JP14TYbMKERAABklVRKHmfT2pz4dMDRRsbi0wHbwwO2V6SzWhCiuqJEO97p18ude0ydr66lSyuXzKbIhI8RfAAAQFZJpeRxNgUfK9MBVy2dZ3s/zBaEyA0Fdf7pk00Hn2wMt9mGqW4AACCrpLJBZrbw+nRAs6Enjv18/I3gAwAAskoqG2Rmi1SmA7oB4RYjIfgAAICsYrXk8cIZk2zuiXulMh3QDQi3GAn/dQEAQFZJZYNMrwv3D2p9U6caOvpGLRTg9RGT8uICbW7rMd0um8JtNiL4AACArBIvebyuMflpWfENMr0qEo2ppr5VdS3dwwLf5rYe3bdxpypLC1VdMVe5oaDnR0yyOdwiMaa6AQCArGN1g0wvipelXteYeN1OvCz18jWNikRjnp8OeFJ+rq48+xRTbQqOm6DaZvcUaID9CD4AACDrWN0g04uslKWuWlCY8Lok4r4RE3PFGd7dO+jopqzIPHeMRwIAAKSZ1Q0yvcRqWeqVS2Z7ejrg7v6IHn/lLUttndyUFZlF8AEAAFnN7AaZbjVS4QLDMCyXpa6uKFF7eF9So0Vumw5opRz30ZzclBWZQfABAADwsNEKF1i1tb1XNy2epbUrylRTv011LSMHiVAwMKQogltYLcd9tPjol1tGspAagg8AAIBHxQsX2PWgHxcvS+3V6YB2ldWOj355fTQQhxB8AAAAPMpM4QIzji5L7bXpgHaW1Y6PfsH7qOoGAADgQVYKFyTLLWWprbJajnskbtmUFakj+AAAAHiQHQv4R+K+stTmWSnHnYhbNmVF6vgvCQAA4EFOTHGTpL85c9qw6nBuXs8zkpPyc02X407E66Nf+CuCDwAAgAc5MQXrpPwc1f/hzzpwcOjrm9t6dN/Gna6s4JaImXLcifhh9At/xVQ3AAAAD7JzCtb4cQGdlJ+j3f2Dw0JPXHxjz+VrGhWJxmw7t1NyQ0GtXVGmZWVFlqe9uWlTVqSOER8AAIAMG2nz0bGml5UXF2hzW4/pc51/+mRJGnKett39evyVt5Jqf+TGnlb6nU5Hl+N+6U89erV7jwYGxw5ubtuUFakLGIZh/6o4HygpKZEktba2ZrgnAADAr8bafHS0DUJ390d03urnTRU4CAUD2nLbRUNCiZXjjB8n/c2Zp+ip197y1MamUvyae29TVqT+fM6IDwAAQAYks/lofHpZe3hAa1eUDXkQt7KAf6SpW1aqwx04KD3+//5sqd+Z5tVNWZE6RnwSYMQHAAA46fYNr5oKLcvKirRq6bwhryUTnuLKiwtGDCHXPtRgacpcskbqN2BFqs/nFDcAAABIMyubj9a1dCncPzjktWQW8IeCAS0rK0o48uL0Bp0j9RvIBKa6AQAApJmV6WXRmKHa5i7dtHjWkNdTnbrl9AadifoNpBvBBwAAIM2s7i2ztb03YYCYkp+jmxbPMh0wrFaHM2O0fgPpwlQ3AACANLM6vcyJaWlVCwot73OTLKen0wHJYMQHAAAgzaxOL3NiWpqV6nBmJdNvt+8JBO8j+AAAAKSZ1ellC2dMcqA3UnVFidrD+yxPwRvLaP0ebS+jzW09um/jTvbVgS2Y6gYAAJBmVqaXhYIBVc0vdKQ/yVaHu/Kjp2j8OPv6HS/Hva4xcbGH+J5Ay9c0KhKNmTo3cCRGfAAAANLMrs1H7ZRsdbhjJoyzrd819a1JjzI1dPSppn4bewLBMjYwTYANTAEAgJPs2Hw0E+zq9+7+iM5b/bypst6hYEBbbruINT9Zig1MAQAAPMiOzUczwa5+p7KXEWAFIz4JMOIDAADSJdw/aGnz0UxLpd/XPtRgqcDD+adP1sPXl1vtMjws1edz1vgAAABkmNXNRzMtlX67aS8jZAeCDwAAyCrsF+MObtrLCNmBOwcAAGQF9otxF7ftZQT/o7gBAADwPfaLcR+37WUE/yP4AAAA37OyXwycFd/LyAyn9zKCvxF8AACAr+3uj6iupdtUm7qWLoX7Bx3qEeKqK0pUXlyQ1HvLiwtUXTHX4R7Bzwg+AADA19gvxr28upcRvIniBgAAwNeSneJ2tK3tvY6Xl6bC3KHws2rpPK1cMtuTexnBOwg+AADA19y4XwwV5obz6l5G8A6CDwAA8DW37RcTrzA32khUvMJce3iAKV6ATQg+AAAgaV6cmpWJ/WJGu073PrfDdIW5VUvnWe4LgEMChmGYW+2XJUpKSiRJra2tGe4JAACZN9rULOnQAnS3Ts3a3R/ReaufN1XgIBQMaMttF5kOc2Ndp/HjpIPGoX+c7gvgN6k+n1PVDQAAjMrrm3+ma7+YZK7TgYPmQo9EhTnALgQfAAAwKq9v/hmJxnTg4EGNXCx5OKv7xZi5TmZtbe915LhANiH4AACAhLy++Wd8FOZXzX/WWAMtAUlV86dbKiZg5TqZ4WSFOSBbEHwAAEBCXt/808wojCEpOG6cpTVKVq6TGU5VmAOyCcEHAAAklMrmn5mWztEqp6a4xaVSYQ7AIQQfAACQkBs3/0xWOkernPy8oWBAVfMLHTs+kC0IPgAAICG3bf5pRjpHq5z8vFYqzAEYjuADAAASKi8usNTODVOz0jlaZfU6jeVjRRMtVZgDMBzBBwAAJFS1oFChYLKFoA9xy9SsdI5WWblOybhw9hTXbQgLeBXBBwAAJJSuzT+dkM7RKivXKRnNb75n+zGBbJX5CbgAAGBM4f5BrW/qVENHnwYGDygvZ7wWzpikqvnOh4zqihK1h/cltWbG6uafTqhaUKj7N7WZKnCQymiVmeuULDcUiQD8ghEfAABcLBKN6fYNr+rc1Zt097M7tbmtR6907tHmth7d9cwOnbt6k27f8Joi0ZhjfcgNBbV2RZmWlRUlnM4VCga0rKzI0uafTkn3aFUy18ksNxSJAPwiYBiGc7tteVhJSYkkqbW1NcM9AQBkq0g0puVrGpMeaUlH6Aj3D6q2uUtb23sdH3myY5QrU9fw6OvUt+8Dvdm73/Rxbr14jm5aPCvl/gB+kOrzOcEnAYIPACDTbt/wqtY1Jr+nzLKyIq1aOs/BHqVHJBpTTX2r6lq6R5ymFgoGVFlaqOqKuUmFlEPH26a6lpH39TF7PCt290d03urnTU+723LbRa5YLwW4QarP54yfAgDgQrv7I6pr6TbVpq6lSyuXzPb0g3IyIzTRmKF1jZ1qDw8kNUKTGwpq1dJ5WrlkdtpGq44Wn3ZnJsi6pUgE4BcEHwAAXKi2aeTRidFEY4Zqm7s8PTWqpr416eIADR19qqnflvQo15T8HN20eFbGro9Xi0QAfkFxAwAAXMhqZbCt7b029yR9rI5yhfsHHeqRvbxaJALwC0Z8AABwIatljL1c/jgbRrncMO0OyFYEHwAAXMhqGWMvlz9OZZTLK8EnLtPT7oBsxFQ3AABcqLy4wFK7hTMm2dyT9MnGUS4A6UPwAQDAhaoWFJreBDMUDKhqfqFDPXJeNo5yAUgfgg8AAC4UL39shtfLH2fjKBeA9OFXJAAAuJRXyx+H+we1vqlTDR19phbuVy0o1P2b2kxv8unlUS4A6UPwAQDApeLlj2vqt6muZeSKZ6FgQJWlhaqumJvx8seRaEw19a2qa+ke1tfNbT26b+POUfvKJp8AnBQwDMNc3cgsUVJSIklqbW3NcE8AADg0iuLm8seRaEzL1zQmPTqVaJ8aK8fpjxywNMIEwFtSfT4n+CRA8AEAIPlpa7dveNXUSM2ysiKtWjpvxJ8dGjkae5TrtkvmaPXT20ccYTryfW4YDQOQOoKPQwg+AIBsNtq0NWloqNgbieq81c+bXpuz5baLRh2RGW2UKz93vC0jTAC8I9Xnc1+s8enr69OHP/xhhcNhzZkzR9u3b890lwAASMjq4v90SWa6WTRmaF1jp9rDA1o4o8BU6Im3r23uGnUDz9E2+bx9w6tJb3ja0NGnmvptCUeYAGQHXwSflStXqqenJ9PdAABgVKku/k+XmvpWU6Hizd79ls6ztb131OCTyO7+iOpauk21qWvp0sols10RLAFkhuf38dm0aZPWrl2rL33pS5nuCgAACcVHUdY1jrxuRfrrKMryNY2KRGNp7V+4f1A/fL5N1/zk9/ovE2t1JOndvRFL5xwYPGCpXW1T4muYSHyECUD28vSIz/vvv6+vfOUrmjt3rv7hH/5B//7v/57pLgEAMCKzoyjpmpo11lqeZFhdLJyXY+0xJNnreDSrI0xOcPt0R8CPPB18ampqtGvXLv3mN79RKBTKdHcAABiRW6dmmSkd7YSFMyZZamd1pMhqOzt5Zboj4EeeDT6vvvqq7rnnHl133XW64IIL9MYbb2S6SwAAjCiVqVlmRyjMjCSYGYUaS0DmRn5CwYCq5hdaOpfVkSKr7exitmgElegAe3ky+Bw8eFBf+tKXNHHiRH3/+99P6VjxsnhH27Vrl2bOnJnSsQEAkNIzNcvsSIKVUajRHJcz3tSISmWp9Sld5cUF2txmvqiR1REmu7h1uiOQLTxZ3OAHP/iBGhsbddddd2nSpMx+iQEAMBanp2ZZKZxgZRTKjr5Kh4JLdcVcy+eqWlCoUDBgqk0qI0x2sDrdMdw/6FCPgOzjuRGfrq4u/dM//ZMuvPBCfeELX0j5eIk2QEo0EgQAgFlOT82yMpLQ/Z61EtSpOHLT01SmcJ2Un6vK0ulaZ6L6XCojTHZI53RHACPz3IjPjTfeqA8++ED/9//+30x3BQCApJQXF1hql8zULKsjCXv2Ry31yaozp5+gLbddpFVL59mybqW6oiTp65rqCJMdUpnuCMAenhvxefLJJzVx4kTdcMMNQ16PRA7tIdDZ2alFixYdfm9eXl66uwgAwBBVCwp1/6Y2U7/xT3ZqltWRhL2R9AafP76919bj5YaCWruiTDX121TXMvI1sGuEyQ5erkQH+IXngo8k7dmzR7/97W9H/Nn7779/+GcHDvBlAQDIPCenZmWqFLVZTkzbyg0FtWrpPK1cMlu1zV3a2t7r2j1xvFqJDvATz/3fZBgj/1brjTfeUHFxsebMmaPt27enuVcAAIyuuqJE7eF9SQUVM1OzrI4I5OeON12COi43NE6R6EHT7ZzaQHRKfo5uWjzL1WthvFqJDvATz63xAQDAi+JTs5aVFSWsSBYKBrSsrMjU/i1WRwROPHaC5p1yguW2VqR72la4f1A/fL5N1z7UoKsefEnXPtSgH73wp4xUSvNiJTrAbzw34gMAgFc5MTUrlZGEirOm6sLv/8b0xqNFBcfq7b9ETJ8zXdO2zO5plA5erEQH+A3BBwCANLNzalYqhROm5Oeocv4p+lXzn5NuW1laqFMm5lpaW5SOaVvxPY1G6198T6P28ICp0bVUOTXdEUByfDPV7bTTTpNhGKzvAQBklfhIghlHjiT88xXzTJeFdvO0LSt7GqWLU9MdASSHER8AADwulZEEK2Whc0NBV07bsrqn0cols9M2pcxLlegAvwkYicqkZbmSkhJJUmtra4Z7AgDA2A6ta0ltT5tw/2DSD+PJTCmLKy8uSMsIxg+fb9Pdz+403e7Wi+e4uiIcgENSfT4n+CRA8AEAeJGZ8JIqO8KWna59qMFSoYfzT5+sh68vd6BHAOyU6vM5U90AAPCRdO5p47ZpW1bLZae7zDaAzCD4AACAlLhlA1Gr5bLTVWYbQGb5pqobAADIbslWpztaOspsA8g8gg8AAPAFN5fZBpB5BB8AAOALqe5pBMDfCD4AAMA3qitKTG/ICiA7EHwAAIBvxDdkXVZWlHDaWygY0LKyorTsLQTAPShjAgAAfMVtZbYBuAPBBwAA+JJbymwDcAemugEAAADwPUZ8AADIUuH+Qa1v6lRDRx9TwQD4HsEHAIAsE4nGVFPfqrqWbkVjxpCfbW7r0X0bd6qytFDVFXNZ/A/ANwg+AABkkUg0puVrGtXQ0ZfwPdGYoXWNnWoPD1D5DIBvsMYHAIAsUlPfOmroOVJDR59q6rc53CMASA+CDwAAWWJ3f0R1Ld2m2tS1dCncP+hQjwAgfZjqBgCAi9lZgKC2qWvYmp6xRGOGapu7KAkNwPMIPgAAuJATBQiSneJ2tK3tvQQfAJ5H8AEAZBxllYdyqgDBwOABS/2x2g4A3ITgAwDIGMoqj8xKAYJVS+eN+d68HGt/7VttBwBuQnEDAEBGxEc11jUmXncSH9VYvqZRkWgszT3MDCcLEJQXF1jq08IZkyy1AwA3IfgAADKCssojS6UAwViqFhQqFAyYOnYoGFDV/EJTbQDAjQg+AIC0o6xyYqkUIBjLSfm5qiydbuq4laXZuc4KgP8QfAAAaefkqIbXOV2AoLqiJOkpb+XFBaqumGupPwDgNqxWBAA4JlG1ts1tPZaOlw1llZ0uQJAbCmrtijLV1G9TXcvIATQUDGRlUQkA/kbwAQDYbqxqbeZWmfxVNpRVLi8usBQMzRQgyA0FtWrpPK1cMlu1zV3a2t5LGXEAvkfwAQDYKpk9aMxNcvurY5IYffD6nkBVCwp1/6Y2U1MBrRYgmJKfo5sWz/L9KBoASAQfAIDNzFRrM2u0ER+/7AkUL0CwrjH59UwUIACAsVHcAABgGyvV2szY9tbeESu7+W1PIAoQAID9CD4AANtYqdZmxoGDI1d289ueQPECBMvKihLuuxMKBrSsrEhrV5S5egQLANyCqW4AANs4NcXtSEdXdrO6J9DKJbNdPT2MAgQAYC+CDwDANumounb0OVLZE8gLi/opQAAA9mCqGwDANlb3oEnlHFZHmba299rRHQCARxB8AAC2SXZBfiqO3q/G6ihTNuwJBAD4K4IPAMA2VQsKEy7Gt8NI+9VYHWVKx+gUAMA9CD4AANvE96Bxykj71VgdZTp65AgA4G8EHwCArczsQSNJyY4PJdqvxsoo00gjRwAAfyP4AABsdeQeNOOT+FsmXo8tUXQZa78aK6NMI40cAQD8jQnOAADbxfegef+DmB7/f39Oqo0h6czpJ+iEY0Km96uprihRe3hfUhXeEo0cAQD8jeADAHDE7v6InnrtLVNt/vj2Xm257SLTozHxUaaa+m2qaxl5X59QMKDK0kJVV8wdceQIAOBvBB8AgCPSvbFofJRp5ZLZqm3u0tb2XtMjRwAA/yL4AAAckcrGolaCT9yU/BzdtHhWSscAAPgPxQ0AAI5gY1EAgJsQfAAAjmBjUQCAmxB8AACOYGNRAICbEHwAAI5gY1EAgJsQfAAAjmBjUQCAmxB8AACOqa4oSXrKGxuLAgCcZGvw+d73vqe3337bzkMCADwsvrHosrKihNPeQsGAlpUVae2KMjYWBQA4JmAYhrnd5UYxbtw4jR8/Xpdddpm+9KUv6VOf+pQCAXPzu92ipKREktTa2prhngCAP4T7B9lYFABgWarP57YGn5qaGv385z/Xm2++qUAgoGnTpun666/XihUrVFRUZNdp0oLgAwAAALhHqs/ntk51q66uVnt7u37961/rqquu0u7du/Wd73xHM2bM0KWXXqrHHntMsVjMzlMCAAAAwJhsL24QCAR0ySWXqK6uTt3d3Vq9erVmzpypp59+WpWVlTrllFN0++23609/+pPdpwYAAACAETla1W3KlCn6xje+oR07dug3v/mNqqqqtHv3bn3/+9/XnDlzdNFFF+mxxx5zsgsAAAAAkJ5y1h0dHXr22We1efNmSZJhGJo6dapeeOEFVVZWqry8XN3d3enoCgAAAIAs5FjwiUajqq2t1ZIlS3T66afre9/7nt5//33dcsst2rZtm7q7u/Xiiy/qU5/6lJqamnTzzTc71RUAAAAAWW683Qf84x//qP/4j//Qww8/rN7eXhmGoYULF+orX/mKqqqqlJube/i95557rp588kktXLhQL7zwgt1dAQAAAABJNgef888/X1u2bJFhGDr++OP1la98RV/5ylc0b968UduVlJSoqanJzq4AAAAAwGG2Bp+XXnpJpaWl+vKXv6zPfOYzOvbYY5Nq98UvflEXXHCBnV0BAAAAgMNsDT6NjY2aP3++6XbnnHOOzjnnHDu7AgAAAACH2VrcwEroAQAAAACnpaWcNQAAAABkEsEHAAAAgO/ZXs4aAGBduH9Q65s61dDRp4HBA8rLGa+FMyapan6hpuTnZLp7AAB4FsEHAFwgEo2ppr5VdS3disaMIT/b3Naj+zbuVGVpoaor5io3FMxQLwEA8C6CDwBkWCQa0/I1jWro6Ev4nmjM0LrGTrWHB7R2RRnhBwAAk1jjAwAZVlPfOmroOVJDR59q6rc53CMAAPyH4AMAGbS7P6K6lm5TbepauhTuH3SoRwAA+BPBBwAyqLapa9ianrFEY4Zqm7sc6hEAAP5E8AGADEp2itvRtrb32twTAAD8jeADABk0MHggre0AAMhWBB8AyKC8HGvFNa22AwAgWxF8ACCDyosLLLVbOGOSzT0BAMDfCD4AkEFVCwoVCgZMtQkFA6qaX+hQjwAA8CfmSgBABp2Un6vK0ula15h8lbbK0kJNyc8Z8lq4f1DrmzrV0NGngcEDyssZr4UzJqlq/vD3AgCQjQg+AJBh1RUlag/vS6rCW3lxgaor5h7+cyQaU019q+pauoeVxd7c1qP7Nu5UZWmhqivmKjcUtL3vAAB4BVPdACDDckNBrV1RpmVlRQmnvYWCAS0rK9LaFWWHA0wkGtPyNY1a15h4L6BozNC6xk4tX9OoSDTm2GcAAMDtAoZhmNs5L0uUlJRIklpbWzPcEwBuF59mtrmtR519+/V+NKZjQkEVFRyrC2ZPMTXdLNw/qNrmLm1t7x1zytrtG141NUVuWVmRVi2dZ+qzAQDgFqk+nxN8EiD4ABhLfJrZr5q7dOBg4veNHxfQ1fPtnW62uz+i81Y/n3CkZyShYEBbbruINT8AAE9K9fmcqW4AYMGR08xGCz2SdOCg/dPNapsST29LJBozVNuc/AgRAAB+QvABAAtq6luTKkZwpIaOPtXUb7Pl/GbPHbe1vdeW8wMA4DUEHwAwaXd/RHUt3Zba1rV0Kdw/mHIfBgYPpLUdAABeR/ABAJOsTDOLs2u6WV6Otd0IrLYDAMDrCD4AYJLVaWZxdkw3Ky8usNRu4YxJKZ8bAAAvIvgAgEmpThezY7pZ1YJCjR838p4/iYwLSFd8dFrK5wYAwIsIPgBgUqrTxVJtH4nG9G/P7VTM5G4EBw3p/6v9AxuZAgCyEsEHAEyyOs0sLpXpZkeW0bayC5udleUAAPASVrkC8IRw/6DWN3WqoaNPA4MHlJczXgtnTFLV/MK0b8hZtaBQ929qs1TgIBQMqGp+oeVzWymjfbS6li6tXDKbjUwBAFmF4APA1SLRmGrqW1XX0j0saGxu69F9G3eqsrRQ1RVzlRsKpqVPJ+XnqrJ0utY1mq/OVllqPailUkb7SPHKcjctnpXysQAA8AqmugFwrSOndSUaXYnGDK1r7NTyNY1pXbtSXVFiespbeXGBqivmWj5nKmW0j8ZGpgCAbEPwAeBaZqZ1pXvtSm4oqLUryrSsrEjjx/gmHT8uoGVlRVq7oiylUalUp7gdiY1MAQDZxrNT3e699169+OKLeu2117R7925FIhGdfPLJWrRokb7xjW+opKQk010EkAIr07rSvXYlNxTUqqXztHLJbNU2d+l3O8Pq7Nuv96MxHRMKqqjgWF0we4pt65DsDCsTguP0w+fbXLFmCgCAdAgYhpW6QJk3efJk7du3T2eeeaZOOeUUSVJra6t27typCRMm6PHHH9enPvUpy8ePB6fW1lZb+gvAnB8+36a7n91put2tF8/x7dqVax9q0Oa2HluONS5wqLz10ULBQNrXTAEAkIxUn889O9XtiSee0HvvvaeGhgZt2LBBGzZs0I4dO/Tggw/qgw8+0Be/+EXFYuxVAXiV1Wldfl67kmoZ7SONFHqkzK2ZAgDAaZ4NPuedd55yc3OHvX7DDTdo1qxZeuutt7Rjx44M9AyAHaxO6/Lz2pWqBYUKBQNpORf7/QAA/MazwWc0weCh6RkTJkzIcE8AWJWXY20JotV2XhAvo50udS1dCvcPpu18AAA4yXfB5xe/+IV27Nih2bNna8aMGZnuDgCLrE7rWjhjks09cRcrZbStiu/3AwCAH3g++Nx11136whe+oKuvvlpnnHGGli9frmnTpumRRx7RuHGe/3hA1rIyrSsUDKhqfqFDPXKHI8top2Pam5/XTAEAsovn54Q888wz2rRp0+E/FxYW6uGHH1ZpaWlS7ROVvd61a5dmzpxpSx8BmBef1rWuMfkRh8rS7CjFfHQZ7drmLr3Zu9+Rc/l5zRQAILt4fkhk48aNMgxD7733nn73u99pzpw5WrRokf7lX/4l010DkCIz07rKiwtUXTHX4R65y5T8HN20eJaKCo517Bx+XjMFAMgunt3HJ5FoNKpzzjlHL7/8shoaGrRgwQJLx2EfH8AdItGYauq3qa6lS9HY8K8rN+w7E+4f1PqmzoxtBnrVgy/plc49jhzbz/siAQC8JdXnc9/9Ki8UCumaa65RS0uL6uvrLQcfAO5w9LSure292rM/qr2RqCQpP3e8ut/br4de7Ehb0Ig7FMpaVdfSPSyUbW7r0X0bd6YllDk1KpMNa6YAANnDd8FHkiZPnixJCofDGe4JALtMyc/R9R8vVvd7+7W1vTejQUM6FHqWr2kcdaPV+Gag7eEBrV1R5lifyosLtLmtx/bjZsuaKQBAdvD8Gp+R/Pa3v5UkihMAPhIPGusaR57yJv01aCxf06hINOZof2rqW0cNPUdq6OhT1U9+79ieOE5sbBqQdNNivkMBAP7hyeCzefNmrV+/XgcODK02FI1G9YMf/EAPP/ywjjnmGF1zzTUZ6iEAu5kNGjX12xzry+7+iOpauk21ebX7Lzpn1SbdvuE120OZExubGpKe+H9v2XpMAAAyyZNT3Xbt2qXrrrtOkydPVmlpqSZNmqSenh699tprevvtt5Wbm6uf//znKixkbjrgB1aCRl1Ll1Yume3IVK3apsSjTqM5cNC5qW/VFSVqD+9LOhwmY2t7L4UNAAC+4ckRnwsvvFDf+ta3NGfOHL366qv61a9+pZdeekkFBQW6+eab9dprr6mqqirT3QRgEytBIxozVNuc/B5AZqQaLpwYkXJiY1P28AEA+IknR3yKi4vZpwfIIlaDhlMjFnYEAidGpEaqgDcweEAdPfu0Z3/U9PHYwwcA4CeeHPEBkF2sBg2nRizsCAROjkjFNzZ9+PpyPXbjefrix4stHWfhjEk29wwAgMwh+ABwPatBw6kRi/LiAluOs7W915bjjMVK1Tf28AEA+A3BB4DrWQ0aTo1Y2FU+Ol1raKxUfWMPHwCA3xB8ALie20Ys7Cofnc41NNUVJUkHyPLiAlVXzHW4RwAApBfBB4CrhfsHVdvUpUnHTTDVzukRCzNBIpF0rqFJpupbKBjQsrIi20ttAwDgBgHDMMxvRpEFSkpKJEmtra0Z7gmQWeH+Qa1v6lRDR58GBg8oL2e8Fs6YpKr5zgaLSDSmmvpW1bV0my5lXV5ckJaH90N93Kb/auyU2S/SUDCgLbddlJHpZOH+wSFV39L13xQAgFSk+nxO8EmA4INsN1bwCAUDqiwtVHXFXNsDRiQa0/I1jabLWDvZp0R290d07qrndeCgua/SK88+Rfdd81FnOgUAgA+l+nzOJg0AhkkmeERjhtY1dqo9PGD76EpNfaup0HPy8bm69pxTMzJiUdvUZTr0SNJpk451oDcAACAR1vgAGMZM8Gjo6FNN/Tbbzr27P6K6lm5TbXr3DWZsmpbVzVVb3nzP5p4AAIDREHwADGEleNS1dCncP2jL+Wubukyv6XFyM9CxuG1zVQAAMDKCD4AhMh08rI6gpGsz0KO5bXNVAAAwMv7mBTBEKsHjpsWzUj6/10ZQyosLtLmtx3Q7O0tZZ6ryHgAAXkLwATBEpoOH10ZQqhYU6v5NbaZGyezaXHW0ynub23p038adaa9yBwCAWzHVDcAQmQ4eVjcFTedmoEc6KT9XlaXTTbWxY3PVeOW9dY2JpybGK+8tX9OoSDSW0vkAAPA6gg+AITIdPKoWFCoUDJhqY9cIilXVFSVJX7fy4gJVV8xN+ZyZrLwHAIAXEXwADJHp4JGpEZRU5IaCWruiTMvKihJeu1AwoGVlRbbseZTpynsAAHgRa3wADBEPHusak6/SZnfwqK4oUXt4X1IjGnaNoKQqNxTUqqXztHLJbNU2d2lre69jhQZSqbxnRwEKAAC8iOADYJhMB4/4CEpN/TbVtYz8kB8KBly5cH9Kfo5uWjzL0YCR6cp7AAB4EcEHwDBuCB7pHEHxmkxX3gMAwIsIPgBG5JbgkY4RFK/JdOU9AAC8iL8FAYzKruDBJpv2ccOmqQAAeA3BB4Cj2GTTfpncNBUAAK+inDUAx7DJpjO8WPIbAIBMI/gAcAybbDonE5umAgDgZQQfAI5gk01npXvTVAAAvI41PgAcwSabznNL5T0AALyA4APAEWyymT6U/AYAYGxMdQPgCDbZBAAAbkLwAeAINtkEAABuQvAB4IhkK44djU02AQCAEwg+ABxRtaAwYbWxRNhkEwAAOIXgA8ARbLIJAADchOADwDFssgkAANyCVcSABeH+Qa1v6lRDRx/7powivslmTf021bWMvK9PKBhQZWmhqivmsskmAABwDMEHMCESjammvlV1Ld3DHuI3t/Xovo07eYj/X0eHw48VnagJ48fpgwMH9UHsIGERAACkFcEHSFIkGtPyNY2jbswZjRla19ip9vCA1q4oc1X4Sdco1WjhUMqeER5GBQEAcJeAYRjDn0ygkpISSVJra2uGewK3uH3Dq1rX2JX0+5eVFWnV0nkO9ig56QwiyYTDuPLiAteFQzsQ/AAAcEaqz+cUNwCSsLs/orqWblNt6lq6FO4fdKhHyYkHkXWNI6+vkf46SrV8TaMi0VhK56upb00q9EhSQ0efauq3pXQ+t0n39QYAAMkj+CDrhfsH9cPn23TtQw266sGXdO1DDfrRC38aElpqmxI/yCYSjRmqbU5+hMgJ6QwiXg2Hdsr24AcAgJsRfJC1ItGYbt/wqs5dvUl3P7tTm9t69ErnHm1u69Fdz+zQuas36fYNrykSjSX9MHu0re29Nvc6eekOIl4Nh3Yh+AEA4G4EH2Qls1OS9r4ftXSegcEDqXQzJekOIl4Mh3bK9uAHAIDbEXyQlcxOSXp3r7XfyuflZK5wYrqDiNWQl8lwaKdsD34AALgdwQdZx8qUpN39EUvnWjhjkqV2dkh3ELEa8jIZDu2U7cEPAAC3I/gg61iZknTQkMYFzJ0nFAyoan6huUY2SncQKS8usNQuk+HQTtke/AAAcDuCD7KO1SlJJ5ncdLKyNLMbVaY7iFQtKFQoaC4dZjoc2inbgx8AAG5H8EHWsTq16EMn5Cb9cFteXKDqirmWzmOXdAeRk/JzVVk63VSbTIdDO2V78AMAwO0IPsg6VqcWHZ8b0toVZVpWVpTwATcUDGhZWZHWrihTbiiYSjdTlokgUl1R4qlwaKdsD34AALgdk8uRdcqLC7S5rcd0u4UzJik3FNSqpfO0csls1TZ3aWt7rwYGDygvZ7wWzpikqvnuepCtrihRe3hfUtP77AgiuaGg1q4oU039NtW1jLyWKhQMqLK0UNUVczMeDu2W7usNAACSFzAMw9wq7yxRUlIiSWptbc1wT2C33f0Rnbf6eVMFDkLBgLbcdpGrQk2yItFYRoJIuH/QE+HQbpm63gAA+F2qz+cEnwQIPv52+4ZXta4x+Y0jl5UVadXSeQ72yHnZGkQyhesNAIC9CD4OIfj4WyQa0/I1jUlPSXLDmh0AAIBslurzOcUNkJXia1G8UqgAAAAAqaG4AbKW1woVAAAAwDqCD7LelPwc3bR4lm5aPCvTXQEAAIBDmOoGAAAAwPcIPgAAAAB8j6lucL1w/6DWN3WqoaOPNTgAAACwhOAD1zq0EWSr6lq6h20EubmtR/dt3MlGkAAAAEgKwQeulMw+O9GYoXWNnWoPD1ByGgAAAKMi+MCVaupbk9pcVJIaOvpUU79Nq5bOc7hXmce0PwAAAGsIPnCd3f0R1bV0m2pT19KllUtm+/bhn2l/AAAAqaGqG1yntqlr2MP9WKIxQ7XNXQ71KLPi0/7WNSa+LvFpf8vXNCoSjaW5hwAAAO7HiA9cJ9kpbkfb2t7ry01IMzXtj2l1AADATwg+cJ2BwQNpbedmmZj2x7Q6AADgR0x1g+vk5VjL41bbuVm6p/0xrQ4AAPgVwQeuU15cYKndwhmTbO5J5qUy7c8KK9PqAAAAvIDgA9epWlCoUDBgqk0oGFDV/EKHepQ56Zz2Z3VaXbh/0PS5AAAA0o3gA9c5KT9XlaXTTbWpLPXngvt0Tvujmh4AAPAzgg9cqbqiJOkpb+XFBaqumOtwjzIjndP+0j2tDgAAIJ0IPnCl3FBQa1eUaVlZUcJpb6FgQMvKirR2RZlvq4ulc9of1fQAAICf+a8MFnwjNxTUqqXztHLJbNU2d2lre2/W7ScTn/a3rjH56WRWp/1RTQ8AAPgZTyxwvSn5Obpp8Sxfbk6ajOqKErWH9yU1FS2VaX/lxQXa3NZjup0fq+kBAAD/Yaob4HLpmvZHNT0AAOBnjPgAHpCOaX/pnFYHAACQbgQfwEOcnvZXXVGiP+0eUNMb74353gWnnejbanoAAMB/mOoGYKhkt/Ixt+UPAABARhF8ABxWU9+qpjfHHu2RpKY331NN/TaHewQAAGAPproBCYT7B7W+qVMNHX1ZUUZ7d39EdS3dptrUtXRp5ZLZpq5Htl1XAADgDgQf+IKdD9ORaEw19a2qa+lWNDZ0Ptfmth7dt3GnKksLVV0x11cbp9Y2dQ37vGOJxgzVNnclteYoW68rAABwB4IPPM3uh+lINKblaxpH3TMnGjO0rrFT7eGBlMpHu00y+wSNZGt775jBJ5uvKwAAcAfW+MCz4g/T6xoTj1TEH6aXr2lUJBob85g19a1JB4CGjj5frXEZGDzgWLtsvq4AAMAdCD7wLLsfpq2ucQn3D5pq41Z5OdYGgMdql+3XFQAAuAPBB57kxMN0Kmtc/KC8uMBSu4UzJo3682y/rgAAwB0IPvAkJx6mU1nj4gdVCwoVCgZMtQkFA6qaXzjqe7L9ugIAAHcg+MCTnHiYdnKNixeclJ+rytLpptpUlo5dNS/brysAAHAHgg88yYmHaafWuHhJdUVJ0lPeyosLVF0xd8z3cV0BAIAb8GQBT3LiYbq8uECb23pMH3OsNS5ekhsKau2KMtXUb1Ndy8jTCUPBwJAS4WPtocR1BQAAbkDwgSc58TBdtaBQ929qM7V2KJk1Ll6TGwpq1dJ5Wrlktmqbu7S1vXfEQBOJxnT7hlfH3EPpxkUzua4AACDjCD7wJCdCSnyNy7rG5KuJJbPGxaum5OfopsWzRtyc1OyGpFeefYp+1Zx8FT4/X1cAAJAZrPGBJzm1EN+JNS5+ZHYPJSn5ctnZfF0BAIBzCD7wLCdCSnyNy7KyooSlnUPBgJaVFWntijLlhoKm+uwHVvZQevyVP+vuq8/iugIAgIwJGIZhbjOULFFSUiJJam1tzXBPMJpINGZqIb4Z4f7BUde4ZKsfPt+mu5/dabrdrRfP0U2LZ3FdAQCAJak+nxN8EiD4eAsP0+lz7UMNlgpLnH/6ZD18fbkDPQIAANkg1edzTxY32L9/v5599lnV19erqalJb7zxhmKxmGbNmqVPf/rTWrlypfLy8jLdTaTRaAvxYS82JAUAAF7kyTU+jzzyiK666iqtWbNGBw8e1CWXXKLzzz9fHR0dqq6u1oIFC7R79+5MdxPwJTYkBQAAXuTJ4DNhwgTdcMMN2rlzp15//XXV1tbq6aef1o4dO3T22Wdr+/bt+vrXv57pbgK+lGxBiaOxISkAAMgk363x+f3vf69zzz1XOTk52rt3ryZMmGDpOKzxsSbcP6j1TZ1q6OhjrY1P7e6P6LzVz5veQ2nLbRdxDwAAAMuyco3PaM466yxJ0uDgoHp7ezV16tQM9yg7HKqu1qq6lu5hD8Sb23p038adlqurwV3Y6BUAAHiRJ6e6jaa9vV2SFAqFVFBgbUoOzIlEY1q+plHrGkcuKS1J0ZihdY2dWr6mUZFoLM09hN3Y6BUAAHiN74LP/fffL0m65JJLlJPDb5jToaa+VQ0dfUm9t6GjTzX12xzuEZzGRq8AAMBrfLXG59e//rX+5m/+RuPHj1dTU9PhaW+jic8VPNquXbs0c+ZM1viMIRPrPVhH5C7soQQAANKBNT7/649//KM+97nPyTAM3XXXXUmFHqSutinx9LZEojFDtc1dpvfcYR2RdU6GRfZQAgAAXuCL4NPd3a1LLrlE7733nlauXKlbbrkl6baJEmOikSAMlewUt6Ntbe819aAcX0c02vni64jawwNMr/pfhEUAAIBDPL/Gp6enR0uWLFFnZ6euu+463X333ZnuUlYZGDyQlnasIzKPohMAAAB/5eng09/fr0996lPavn27li5dqp/+9KcKBEZeaA1n5OVYGzQ00253f0R1Ld2mjl/X0qVw/6DZbvkKYREAAOCvPBt8BgcHdcUVV6i5uVkXX3yx1q1bp2CQqTrplmxJ46MtnDEp6femso4oWxEWAQAAhvJk8InFYlq2bJleeOEFnX/++dqwYYMmTJiQ6W5lpaoFhQnLGScSCgZUNb8w6fenso4oWxEWAQAAhvJkcYMf/vCHeuyxxyRJkydP1o033jji++6++25Nnjw5nV3LOifl56qydLrWNSb/wFxZaq6SWLrWEflJuopOAAAAeIUng8977713+N/jAWgkd955J8EnDaorStQe3pfUw3Z5cYGqK+aaOn461hH5DWERAABgKE9OdbvzzjtlGMaY/5x22mmZ7mpWyA0FtXZFmZaVFSWc9hYKBrSsrMhSmel0rCPyG8IiAADAUDzlwBa5oaBWLZ2nlUtmq7a5S1vbe23bKLNqQaHu39Rmas2K2XVEflNeXKDNbT2m22VzWAQAAP5G8IGtpuTn6KbFs2xdJ5KOdUR+Q1gEAAAYypNT3ZB9qitKkp7yZmUdkd/Ew6IZ2R4WAQCAvxF84AlOryPyI8IiAADAXwUMwzC32UeWKCkpkSS1trZmuCc4Wrh/0PZ1RH4VicZUU79NdS0j7+sTCgZUWVqo6oq5hEUAAOBqqT6fE3wSIPjATwiLAADA61J9Pqe4AWCjcP+g1jd1qqGjz1UBw4miEwAAAF5C8AFscGhKWavqWrqHTSnb3Naj+zbuZEoZAABABhF8gBRFojEtX9Ooho6+hO+Jxgyta+xUe3iA4gsAAAAZQFU3IEU19a2jhp4jNXT0qaZ+m8M9AgAAwNEIPkAKdvdHVNfSbapNXUuXwv2DDvUIAAAAIyH4ACmobRq5TPRoojFDtc1dDvUIAAAAI2GND1zLrRXSjpTsFLejbW3vpcIaAABAGhF84DpeqpA2MHggre0AAABgDcEHruK1Cml5Odb+F7LaDgAAANawxgeu4rUKaeXFBZbaLZwxyeaeAAAAYDQEH7iGFyukVS0oVCgYMNUmFAyoan6hQz0CAADASAg+cA0vVkg7KT9XlaXTTbWpLHVPcQYAAIBsQfCBa6RSIS2TqitKkp7yVl5coOqKuQ73CAAAAEcj+MA1vFohLTcU1NoVZVpWVpRw2lsoGNCysqKMF2MAAADIVpSWgmt4uUJabiioVUvnaeWS2apt7tLW9l7X7j0EAACQjTL/xAj8r/LiAm1u6zHdzk0V0qbk5+imxbPYnBQAAMBlCD5wjaoFhbp/U5upAgdWKqSF+we1vqlTDR19jMoAAABkCYIPXCNeIW1dY/JV2sxUSItEY6qpb1VdS/ewcLW5rUf3bdypytJCVVfMZR0OAACAz1DcAK7iVIW0SDSm5Wsata4xccnsaMzQusZOLV/TqEg0lnSfAQAA4H4EH7iKUxXSaupbky6X3dDRp5r6bUn3GQAAAO7HVDe4jt0V0nb3R1TX0m2qD3UtXVq5ZDZrfgAAAHyC4APXsqtCWm1T4ultiURjhmqbu6jOBgAA4BNMdYPvJTvF7Whb23tt7gkAAAAyhREfZEQ6S0oPDB5IazsAAAC4D8EHtkkmzGSipHRejrXb3Go7AAAAuA9PdkhZsmHmm5fM0Zcfbhl16lm8pHR7eMBU1bbRlBcXaHNbj+l2C2dMSvncAAAAcAfW+CAlZvbHWfJvv8tISemqBYUJS2MnEgoGVDW/0JbzAwAAIPMIPkiJmf1xwv2Dpo5d19Jlus1ITsrPVWXpdFNtKkvtX2sEAACAzGGqGyyzsj+OGWZLSo+2xqi6okTt4X1JhbTy4gJVV8xNtfsAAABwEYIPLLOyP45ZW9t7xww+ya4x+vdrS7X66R2qaxm536FgwPbCCgAAAHAHgg8ss7o/jhljlZSOrzEyUzBh5ZLZqm3u0tb2XsdLaQMAAMAdCD6wLB373IxVUtrMGqN4wYRVS+fppsWzkp5CBwAAAO+juAEsS8c+N6OVlLayxsiuggkAAADwFoIPLCsvLnD0+GOVlLayxiheMAEAAADZheADy6zsj2PGWCWlra4x2trea7VLAAAA8CiCDyyzsj/OSUkWD0impLTVNUbpWJsEAAAAdyH4ICXVFSVJT3krLy7Qs39/gZaVFSUcKQoFA1pWVqS1K8rGLCltdY1ROtYmAQAAwF14AkRKckNBrV1Rppr6bUnvj7Nq6TxbSkqXFxdoc1uP6T6PVjABAAAA/hQwDMPZHSg9qqSkRJLU2tqa4Z54R7h/MK374+zuj+i81c+bKnAQCga05baL2K8HAADAY1J9PmfEB7aZkp+T1v1x4muM1jUmX6VtrIIJAAAA8CeCjw+F+we1vqlTDR19aRl5yaTqihK1h/clVeEtmYIJAAAA8CemuiXgxalukWhMNfWtqmvpTmqtjV8c+tzJrzECAACA96T6fE7wScBrwScSjWn5msakRz6SqZrmNeleYwQAAID0Ifg4xGvB5/YNr5pa67KsrEirls5zsEcAAACAfVJ9PmcfHx/Y3R9RXUu3qTZ1LV0K9w861CMAAADAXQg+PlDbNPLaltFEY4Zqm5MfIQIAAAC8jODjA8ms6xnJ1vZem3sCAAAAuBPBxwcGBg+ktR0AAADgNezj41Jm9uLJy7H2n9FqOwAAAMBrePJ1mdH24tnc1qP7Nu4ctidNeXGBNrf1mD7XwhmTbOkzAAAA4HZMdXOR+F486xoTFyuIxgyta+zU8jWNikRjkqSqBYUKBQOmzhUKBlQ1vzDlPgMAAABeQPBxkZr61qQLFTR09Kmmfpsk6aT8XFWWTjd1rspSNvUEAABA9iD4uESqe/FUV5SovLggqXblxQWqrphruo8AAACAVxF8XCLVvXhyQ0GtXVGmZWVFCae9hYIBLSsr0toVZYfXBwEAAADZgOIGLpHKXjw3LZ4l6VD4WbV0nlYuma3a5i5tbe8dsyIcAAAAkA0IPi5h5148U/JzdNPiWYcDEQAAAJDtmOrmEuzFAwAAADiH4OMSyRYmOBp78QAAAABjI/i4BHvxAAAAAM4h+LgEe/EAAAAAziH4uAh78QAAAADOIPi4CHvxAAAAAM6gJJjLsBcPAAAAYD+Cj0uxFw8AAABgH4KPy4X7B7W+qVMNHX2M/AAAAAAWEXxcKhKNqaa+VXUt3YrGjCE/29zWo/s27lRlaaGqK+ay1gcAAAAYA8HHhSLRmJavaVRDR1/C90RjhtY1dqo9PEChAwAAAGAMVHVzoZr61lFDz5EaOvpUU7/N4R4BAAAA3kbwcZnd/RHVtXSbalPX0qVw/6BDPQIAAAC8j+DjMrVNXcPW9IwlGjNU29zlUI8AAAAA7yP4uEyyU9yOtrW91+aeAAAAAP5B8HGZgcEDaW0HAAAAZAOCj8vk5VgrtGe1HQAAAJANCD4uU15cYKndwhmTbO4JAAAA4B8EH5epWlCoUDBgqk0oGFDV/EKHegQAAAB4H8HHZU7Kz1Vl6XRTbYoKjlN+LlPdAAAAgEQIPi5UXVFiasrbrvCAlq9pVCQac7BXAAAAgHcRfFwoNxTU2hVlmjnluKTbNHT0qaZ+m4O9AgAAALyL4ONSeyNRdfbtN9WmrqVL4f5Bh3oEAAAAeBfBx6Vqm7oUjRmm2kRjhmqbuxzqEQAAAOBdBB+Xaujos9Rua3uvzT0BAAAAvI/g41IDgwfS2g4AAADwM4KPS+XlWCtPbbUdAAAA4GcEH5cyU876SAtnTLK5JwAAAID3EXxcqmpBoULBgKk2oWBAVfMLHeoRAAAA4F0EH5c6KT9XlaXTTbWpLC3UlPwch3oEAAAAeBfBx8WqK0qSnvJWXlyg6oq5DvcIAAAA8CaCj4vlhoJau6JMy8qKEk57CwUDWlZWpLUrypQbCqa5hwAAAIA3eLYEWEtLi5577jk1NjaqoaFBb731lnJychSJRDLdNVvlhoJatXSeVi6ZrdrmLm1t79XA4AHl5YzXwhmTVDWf6W0AAADAWAKGYRiZ7oQVV155pZ544okhr9kZfEpKSiRJra2tthwPAAAAgHWpPp97dsTnnHPO0VlnnaUFCxZowYIFOvnkkzPdJQAAAAAu5dng881vfjPTXQAAAADgERQ3AAAAAOB7BB8AAAAAvufZqW52iS+SOtquXbs0c+bMNPcGAAAAgBMY8QEAAADge1k/4pOoHF6ikSAAAAAA3sOIDwAAAADfI/gAAAAA8D2CDwAAAADfI/gAAAAA8D2CDwAAAADf82xVt6eeekr//M//POS1Dz74QAsXLjz85zvuuEOXXXZZursGAAAAwGU8G3zC4bAaGhqGvGYYxpDXwuFwursFAAAAwIUChmEYme6EG8X38Um0zw8AAACA9En1+Zzgk0B+fr6i0ahmzpyZ6a4AAAAAWW/Xrl0KhULq7++31J7iBgkcd9xxCoVCth93165d2rVrl+3HBdfWaVxf53BtncX1dQ7X1jlcW2dxfZ3j5LUNhUI67rjjLLdnxCfNmELnHK6ts7i+zuHaOovr6xyurXO4ts7i+jrHzdeWER8AAAAAvkfwAQAAAOB7BB8AAAAAvkfwAQAAAOB7BB8AAAAAvkdVNwAAAAC+x4gPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+KRg3759evjhh3XzzTerrKxMOTk5CgQCWr16dUrHffLJJ3XhhRfqhBNO0PHHH68LL7xQTz755Kht/vjHP+rqq6/WlClTdMwxx2jevHn6t3/7Nx08eDClvrjBli1bdOmll6qgoEB5eXkqKyvT2rVrTR/ntNNOUyAQGPWfGTNmDGnzxhtvjPr+k08+2a6PmRF2Xduf//zno16nv/3bv03Y1q/3rl3XtqWlRXfeeafOP/98TZs2TTk5OSosLNTnPvc5vfrqqyO28cN9G4lEVF1drdmzZys3N1fTpk3TihUr1N3dbfpYe/bs0de//nWdeuqpysnJ0amnnqpbbrlFe/bsSdjm4MGDuu+++zRv3jwdc8wxmjJliq6++mpt27YthU/lDnZc2z179uiRRx7RZz7zGc2dO1fHHXec8vPzVV5ervvvv1/RaHTEdl/4whdGvTd//OMf2/UxM8aue3esv7O2b98+Yjvu3dGN9fdV/J9f/OIXQ9r5+d5taWnR6tWrtXTpUp1yyikKBALKzc21fDw3f+eOt/VoWaatrU2f//znbT3mAw88oFtuuUXjx4/XJz/5SeXk5OjZZ59VRUWF7r//fn3ta18b1mbr1q266KKLtH//fpWVlem0007T7373O61cuVIvvfSSfvWrXykQCNjaz3R57LHHdPXVV+vgwYO64IILNHnyZG3atElf+MIX9Ic//EH33ntv0seqrKxUT0/PiD/77W9/qzfeeEPnn3/+iD//0Ic+pEsuuWTY6yeccELS53cbO69t3FlnnaWPfvSjw14vLy8f8f1+vXfturYHDhzQ/PnzJUmTJ09WWVmZjj32WL3yyiv65S9/qdraWj3yyCOqrKwcsb1X79tIJKKLLrpIW7Zs0dSpU3XFFVfojTfe0M9+9jM9+eST+v3vf6+ZM2cmdaze3l6dc845amtr04wZM3TllVeqtbVVDzzwgH79619r69atmjRp0pA2hmHommuuUV1dnSZOnKjLLrtMPT09evTRR/XUU0/phRdeSHhPu51d1/buu+/Wv/zLv2jcuHE6++yzVVFRoXA4rJdeekmNjY2qq6vTM888o2OPPXbE9hdffPGIAXzOnDkpf8ZMsvPejVu+fPmIr4/0/zH37tjXdtasWQmv6V/+8hc9/vjjkqSPf/zjI77Hj/fuP//zP+uJJ56w5Viu/841YNmf/vQn4/rrrzd+8pOfGC+//LLxj//4j4YkY9WqVZaOt2PHDmP8+PFGTk6OsWXLliGvT5o0yRg/fryxc+fOIW2i0agxc+ZMQ5Jx7733Hn69v7/fOOeccwxJxpo1a6x9wAzr6+szTjjhBEOS8eijjx5+/Z133jFmzZplSDKef/75lM8Ti8WMadOmGZKM5557bsjPOjo6DEnGhRdemPJ53MTua/uzn/3MkGRUV1cn3cav966d1zYajRrl5eXGk08+acRiscOvx2Kxw983+fn5RjgcHtLO6/ftHXfcYUgyzjnnHKO/v//w6/fcc48hybjggguSPta1115rSDKWLl1qRKPRw6/ffPPNhiTj85///LA2Dz30kCHJOP3004133nnn8Ot1dXWGJGPmzJlDjuUldl3bVatWGd/61reM7u7uIa/v3LnTKCoqMiQZt99++7B2y5cvNyQZL7zwQkqfw63svHdPPfVUw+xjGvduah588EFDknHeeecN+5mf793Vq1cb3/72t436+nrjnXfeMSQZOTk5lo7l9u9cgo+NqqurUwo+N954oyHJuOWWW4b97N577zUkGV/96leHvF5bW2tIMs4666xhbV5++WVDknHGGWdY6k+mff/73zckGVdcccWwn23YsMGQZPzN3/xNyud59tlnDUnGtGnThjxcGob3HyATsfvaWgk+fr1303XfHjx40Pjwhz9sSDJ+/vOfD/mZl+/bDz74wJg4caIhyXj55ZeH/fzMM880JBnNzc1jHuvtt982xo0bZ4RCoSF/mRqGYUQiEWPKlClGMBgc9rO5c+cakozHHnts2DEvv/xyQ5JRV1dn7oO5gJ3XdjSPPPKIIck47bTThv3Mzw+Pdl9fK8GHeze1e/fcc881JBk//vGPh/3Mz/fu0awGHy9857LGx0Xi63hGmrZy9dVXS5Lq6+uTbnP22WdrxowZev311/XGG2/Y3FvnjfbZLrvsMuXm5mrjxo2KRCIpnec///M/JUmf/exnNW5cdvwvka5ra7UPXr5303VtA4GA5s2bJ0l66623UjqWm7z44ovas2ePZs6cqbPPPnvYz+PX9ejvwpH8z//8z+Hphh/60IeG/CwnJ0cVFRWKxWL6n//5n8Ovd3R0aNu2bTrmmGN02WWXpXR+t7Hz2o7mrLPOkuSv+zIZ6bq+iXDvpvbZOjo6tGXLFk2YMEFVVVWWj5PNvPCdyxofl9izZ486OzslacT/qadPn67JkyfrzTff1F/+8pfDc3v/8Ic/SJI+9rGPjXjcj33sY2pvb9cf/vAHnXbaac503iHxhdsjfbYJEybojDPOUHNzs3bs2HH4L1qz3n//fT322GOSpM997nMJ3/fuu++qurpab7/9tk444QSVl5fr8ssv14QJEyydN9OcurYtLS269dZbtXfvXp188sn6xCc+oQsvvHDE9/r13k3HfRvX3t4uSQmLFXjxvk3mvjjyfakea82aNUOOFf/3M844Q6FQKKXzu42d13Y0Y92XkrRhwwY9+uijisViKi4uVkVFhT784Q+ndN5Mc+r63nXXXdq1a5dycnJUUlKiq666SlOmTEl4fu5da+K/BL3ssst04oknJnyfH+9du3jhO5fg4xLx0HPiiSfquOOOG/E906dPV09Pjzo7Ow//pjfebvr06QnbHPk+r9i7d+/h6h+jfbbm5mZ1dnZafoB8/PHH1d/frzPPPFNnnnlmwvdt375d3/nOd4a8VlRUpNraWs8tFHXy2j755JNDKhB+5zvf0YUXXqj169cP++2PH+/ddN230qHfgLa0tGjChAkjFjCQvHnf2nlfWDmWH+/LuHR9tvvvv1+SdMUVVyR8zw9+8IMhf/7mN7+pG264Qffff7/Gj/fmo4lT1/cb3/jGkD///d//vR544AFdf/31aTm/G6Tjs/3yl7+UJF177bWjvs+P965dvPCdmx3zejxgYGBAkhJWwJF0OBDF35tMu5HaeMGR/XXysz388MOSEn/R5eTk6IYbbtBvfvMbvfvuu/rLX/6i3//+97r00kvV2dmpSy65xHNTsZy4tlOnTtWdd96pV155RX/5y1/0zjvv6L//+7/14Q9/WL/97W912WWXKRaLjdgPP9276bpv9+7dqxUrVkg69BA0derUIT/38n1r531h5Vh+vC/j0vHZfvzjH2vjxo2aOHGibrvttmE/P/vss/XjH/9YO3fu1P79+9Xe3q4f/ehHmjhxoh588EHdeuutls+daXZf38svv1wbNmzQm2++qf379+v111/XypUrNTg4qC9+8YuHq485dX43cfqzNTY2aseOHTrxxBNHnG4l+fvetYsXvnOzOppWVlbq9ddfN9XmF7/4hcrKymzvi2EYkjRq6d74e0aSqN1obZyWyvVNpt+pfrZwOKznnntO48aN02c+85kR3zN16lQ9+OCDQ15buHChnnrqKX32s5/VI488ou9973v693//95T6Ypbbru3FF1+siy+++PCfjz/+eFVUVGjx4sUqLS1VS0uL1q9fP+J1dtu967Zre7RYLKbPfOYzamtrU1lZ2bARHcm9920yxvouNHP9rBwrme9ir7Lz2o7kt7/9rW655RYFAgGtWbNG06ZNG/aeW265Zcifi4uLdeONN+qCCy5QaWmpfvCDH2jlypUqLCxMqS+ZYPf1feCBB4b8uaSkRPfcc4/mzJmjL3/5y/rmN7+pK6+8Munze5nT9258mts111yTcCqwn+9du3jhOzerg88bb7yhHTt2mGqzf/9+R/qSn58v6dCmqGOdOy8v7/BreXl5eu+99xK2G6lNuqRyfePXI/7a8ccfn/C9Vj/bunXrdODAAS1ZsmTEv6DH8q1vfUuPPPKInnnmGUvnT4Xbr21cXl6evva1r+mrX/2qnnnmmSHBx633rtuv7d/93d/pqaee0pw5c/TUU0+ZXq+Tyfs2GWN9F5q5flaONVab+OuZ+E5NlZ3X9mivvvqqrrzySn3wwQd64IEHdNVVV5lqf8YZZ+jyyy9XXV2dNm7cqOuuu850HzLNyet7pC9+8Yu64447tHPnTnV0dKi4uDip83PvjuzAgQNav369pLGnuY3ED/euXbzwnZvVU92am5tlHCrpnfQ/ixYtcqQvRUVFkjTqg2B8Z+L4e4/890S7Fo/UJl1Sub7HH3/84QIOTn22+G94RitqMJrTTz9dkvT2229bap8Kt1/bIyW6Tm69d918bW+99VatWbNGhYWFeu655zR58mTTx8jkfZsMO+8LK8dy631pB6c+265du3TxxRdrz549uvPOO3XzzTdb6p/b782xpOveGTdu3OGNOo+8Vty71j7bs88+q927d2vGjBk699xzLfXP6/euXbzwnZvVwcdNJk6cePg/6iuvvDLs593d3erp6VFRUdGQ3Zrji6NffvnlEY8bf320hftuNdpni0ajev3115WTk2Npt+SdO3eqqalJxx57rJYuXWqpf++9954kb/72zMlre7RE18mv965T13bVqlW6++67ddJJJ+m5556zPJ3C7fetnfeFlWPF27z++uuKRqMpnd9tnPh/7q233tKSJUv0zjvv6JZbblF1dbXl/rn93hxLOr/TRrpW3LvWPluqvwSVvH/v2sUT37mWdwDCMKluYHrDDTeMuYHpjTfeOOT19evXj7kJ5Ny5cy31J9P+9V//dcyNIC+99FJLx47vAP3Zz37Wcv9+9KMfGZKMT37yk5aPkSlOXtujXX311YYk47vf/e6Q1/167zpxbX/yk58YkoyJEycar7zySkr9c/t9Ozg4aJxwwgljblTY2Ng45rHeeustY9y4ccaECROMd999d8jP4pvpjRs3znj77beH/OwjH/nImJvp1dbWmvtgLmDntTUMw+jr6zPOOOMMQ5Jx3XXXGQcPHrTct0gkYhQWFhqSjBdffNHycTLJ7uubyOuvv24EAgHj2GOPNQYHB4f8jHvX3LXt7+83jj32WEOSsXPnTkt988O9ezRZ3MDUC9+5BB8bJRt85syZY8yZM8fo7u4e8vr27duNYDBo5OTkGL///e8Pv75z505j0qRJRjAYNLZv3z6kzQcffGAUFxcbkox777338OsDAwPGOeecY0gy/uM//sOGT5d+vb29xvHHH29IMh599NHDr7/77rvGrFmzDEnGxo0bh7VLdH2PNGPGDEOS8fTTT4/ah7Vr1xpdXV3DXn/00UeN/Px8Q5KxYcMGE5/KHey+tvfff7/R398/5LUPPvjAuPPOOw1JxjHHHDOsjV/vXbuv7a9+9Stj3LhxRl5enrFly5ak+uD1+/Yf//EfDUnGueeeawwMDBx+/Z577jEkGR//+MeHvP8HP/iBMWfOHOO2224bdqzPfvazhiTj05/+tBGNRg+//rWvfc2QZHzuc58b1uanP/2pIck4/fTTh/zl/eijjxqSjOLiYuODDz6w46OmnV3Xdt++fcbChQsNSUZVVZVx4MCBMc+9fft24/HHHx/23t27dxtXXnnl4V+EpBKgMs2u6/v0008bzc3Nw47/hz/84fBD4te+9rVhP+fe/avRvhfi1q5da0gyFi5cOOq5s+HePdJYwcfL37kEnxRdeeWVRnl5uVFeXm6ccsophiSjsLDw8GtXXnnlsDaSDElGR0fHsJ/FR3bGjx9vfOpTnzKuuOIK45hjjhn2cHikl1566fB7ysvLjaqqKmPq1KmGJOPKK680YrGY3R87berq6oxx48YZgUDAWLRokVFZWWlMnDgx4Ze+YYx+fQ3j0PWSZJx88slj/mV94YUXGuPGjTPmzp1rXHrppcbSpUuND3/4w4fPceutt6b6ETPGzmsbDzelpaXG0qVLjUsvvdSYNm2aIcnIzc0dEgCO5Nd7165r++677xoTJkwwJBnz5s0zli9fPuI/R/+WzOv37fvvv2+Ul5cbkoypU6caVVVVh/88adIko62tbcj74790Wr58+bBjhcNhY+bMmYYkY+bMmcY111xzeJRi5syZRjgcHtYmFosZV111lSHJOPHEE43Kykpj0aJFRiAQMHJzc42XXnrJqY/uOLuu7de//nVDkhEMBo3PfOYzCe/NI73wwguHz3PeeecZVVVVxqJFiw6H8enTpxs7duxw+Ao4y67rG3/91FNPNT7xiU8Y11xzjVFWVmaMHz/ekGRceOGFxr59+4adn3v3r0b7XohbsmSJIcn40Y9+NOq5/X7vPvnkk4efW+PXNBAIDHntySefPPx+L3/nEnxSdOqppx5+mBjpn1NPPXVYm7EezP/7v//bOP/88428vDwjLy/P+PjHP2488cQTo/bj9ddfNz796U8bkyZNMnJycoy5c+cad999d1K/hXO7F1980bjkkkuMiRMnGscee6xRWlpqrFmzJuH7x7q+8SmFf//3fz/muf/zP//TqKysNGbNmmUcf/zxRigUMqZNm2YsXbrUeO6556x+JNew69p++9vfNpYsWWIUFhYaxxxzjJGbm2vMmjXL+PKXvzxslPJofr137bi2HR0do36/xP+prq4eciw/3Lf79+837rjjDmPmzJnGhAkTjA996EPG8uXLjc7OzmHvHesBp6+vz7j55puNwsJCY8KECUZhYaHx1a9+1ejt7U14/gMHDhj33HOPUVJSYuTm5hqTJk0yli5darz++ut2fcSMsePaLl++PKl780h//vOfja9//evGwoULjZNPPtkIhUJGXl6e8bGPfcyorq42+vr6nPzYaWPH9d2yZYuxYsUKY968ecakSZOM8ePHGwUFBcaiRYuMn/70p6N+P3LvHjLW98Jbb71lBINBIxQKGT09PaOe1+/37s9+9rMx/1/+2c9+dvj9Xv7ODRhGBjd6AQAAAIA0oKobAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAAADwPYIPAAAAAN8j+AAAfOeaa65RIBDQN7/5zWE/2759u4499lgdf/zxam9vz0DvAACZEDAMw8h0JwAAsNN7772nM888U2+99ZY2bdqkRYsWSZKi0ajKy8v1yiuv6Gc/+5m+8IUvZLSfAID0YcQHAOA7J554on7xi19Ikj7/+c9rz549kqR/+qd/0iuvvKLKykpCDwBkGUZ8AAC+9Y1vfEN33XWXli1bpr/7u7/TRRddpJNPPlmvvfaaCgoKMt09AEAaEXwAAL71wQcfaOHChXrllVd0/PHHq7+/X88++6w++clPZrprAIA0Y6obAMC3JkyYoJ///OeSpL179+qrX/0qoQcAshTBBwDga+vXrz/876+88ooOHjyYwd4AADKF4AMA8K3Nmzdr9erVmjZtmj7xiU/oxRdf1OrVqzPdLQBABrDGBwDgS3v37tWZZ56pzs5OPf3005o3b57mzZunvXv3asuWLZo/f36muwgASCNGfAAAvnTjjTfqzTff1M0336z/83/+j6ZOnaqf/vSnikaj+uxnP6v9+/dnuosAgDQi+AAAfOe//uu/9Mtf/lIlJSX613/918OvX3XVVbruuuu0c+dOrVy5MoM9BACkG1PdAAC+0tXVpTPPPFP79+9XQ0ODPvrRjw75+cDAgM466yy1t7friSee0OWXX56ZjgIA0orgAwAAAMD3mOoGAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB8j+ADAAAAwPcIPgAAAAB87/8HjmslpoubTaYAAAAASUVORK5CYII=\n", - "text/plain": [ - "

" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "plt.figure(dpi=150)\n", "plt.scatter(x[:, 1], y)\n", @@ -262,7 +225,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -289,7 +252,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -310,20 +273,9 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "tensor(63.0779)" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "y_hat = x @ w_real\n", "# Initial mean-squared error\n", @@ -332,20 +284,9 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "plt.figure(dpi=150)\n", "plt.scatter(x[:, 1], y, label=\"y\")\n", @@ -356,21 +297,9 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Parameter containing:\n", - "tensor([-3., -5.], requires_grad=True)" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "w = nn.Parameter(w_real)\n", "w" @@ -385,22 +314,9 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Load the image file\n", "with open(\"figs/Gradient_descent2.png\", \"rb\") as f:\n", @@ -442,7 +358,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -475,7 +391,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -489,7 +405,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -511,7 +427,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -556,1345 +472,9 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(HTML(f'
{animation.to_html5_video()}
'))" ] @@ -1908,20 +488,9 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "plt.figure(dpi=150)\n", "plt.plot(np.array(losses))\n", From c9a2bec207f4b269f5968515395cd8548ea1cb35 Mon Sep 17 00:00:00 2001 From: Feiyu Lu Date: Mon, 17 Jul 2023 21:23:20 -0400 Subject: [PATCH 07/10] Adding description of DA --- notebooks/DA_demo_L96.ipynb | 56 ++++++++++++++++++++++++++++++++---- notebooks/figs/DA_step.png | Bin 0 -> 368756 bytes 2 files changed, 51 insertions(+), 5 deletions(-) create mode 100644 notebooks/figs/DA_step.png diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 37d6e61a..611ed9df 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -44,6 +44,52 @@ "```" ] }, + { + "cell_type": "markdown", + "id": "c33e3435", + "metadata": {}, + "source": [ + "# What is DA? Why do we do it?\n", + "\n", + "Data assimilation is an approach for combining data (observations) with prior knowledge (from a physical model) to obtain an estimate of the true state of a system. We use data assimilation to generate accurate initial conditions for weather and climate predictions, and to produce reanalysis products (state estimates) of the atmosphere-ocean-sea ice-land system. \n", + "\n", + "Conceptually, data assimilation follows the Bayes' Rule:\n", + "\n", + "\\begin{align}\n", + "\\ P(X|Obs)=\\frac{P(Obs|X)P(X)}{P(Obs)}\n", + "\\end{align}\n", + "\n", + "where $P(X|Obs)$ is the posterior distribution, or the analysis in DA terms, and $P(X)$ is the prior distribution, or the forecast in DA terms. $P(Obs|X)$ is the observation distribution given the prior. Below is a simple schematic representation of one DA step.\n", + "\n", + "```{figure} figs/DA_step.png\n", + "```\n" + ] + }, + { + "cell_type": "markdown", + "id": "208a8f14", + "metadata": {}, + "source": [ + "# Design of the data assimilation experiments in L96\n", + "\n", + "We use the 2-scale L96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". This is what we call an idealized biased-model framework in DA research. Our DA model is biased compared to our truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", + "\n", + "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", + "1. Generate a “truth” signal from 2-scale L96 model\n", + "2. Specify a biased “GCM”model for performing DA\n", + " * Choose P (to start, use GCM with P=0).\n", + " * Choose F_GCM (to start, use F_GCM=F).\n", + "3. Collect sparse and noisy observations, sampled from “truth”\n", + " * Specify observation density in space, frequency in time\n", + " * Specify observational error\n", + "4. Perform DA using a method of choice\n", + " * Choose DA method: EnKF, 3DVAR, Hybrid EnKF\n", + " * Specify DA setup: ensemble members, localization, inflation\n", + "5. Assess DA performance\n", + " * RMSE of DA experiment relative to truth\n", + "6. Analyze DA increments to assess GCM model error (optional)\n" + ] + }, { "cell_type": "markdown", "id": "66584b6f", @@ -96,11 +142,11 @@ " seasonal = False # Option for adding a seasonal cycle to the forcing in the L96 truth model\n", " B_loc = 5 # Spatial localization radius for DA\n", " DA = \"EnKF\" # DA method\n", - " nens = 100 # Number of ensemble members for DA\n", + " nens = 500 # Number of ensemble members for DA\n", " inflate_opt = \"relaxation\" # Method for DA model covariance inflation\n", - " inflate_factor = 0.2 # Inflation factor\n", - " hybrid_factor = 0.1 # Inflation factor for hybrid EnKF method\n", - " param_DA = False # Switch to parameter estimation with DA\n", + " inflate_factor = 0.65 # Inflation factor\n", + " hybrid_factor = 0.1 # Weighting factor for hybrid EnKF method (weight of static B matrix)\n", + " param_DA = False # Switch to turn on parameter estimation with DA\n", " param_sd = [0.01, 0.02, 0.1, 0.5] # Polynomal parameter standard deviation\n", " param_inflate = \"multiplicative\" # Method for parameter variance inflation\n", " param_inf_factor = 0.02 # Parameter inflation factor\n", @@ -1140,7 +1186,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.8.12" } }, "nbformat": 4, diff --git a/notebooks/figs/DA_step.png b/notebooks/figs/DA_step.png new file mode 100644 index 0000000000000000000000000000000000000000..937fecb9d7f5888530369757c5cec0dba408c1c1 GIT binary patch literal 368756 zcmeFZXIN9));3I&q6i2|kwB0ZkPZp~LO?+fsfyC27m<#%&=Dje9i&NBL_~V;HFN}| zBR%w9LJjp>>~r?ndamd3{rmlR;KHonTr+cyIm$i8Jr;qg%5qmP-@J^2gL75>q0AE; z970AM90Dd{Lf|)amF#@L3+}5Ya`$m^yFtsq8-G(xc{3#?oZG-PG0r7iN*w%)A;32d z?oFIae_i9?Ji?{_&-D{rj(?BA!@)sX;1K+Kj5hFk@f8F70C)fU6+adCpBYo}{vJ)p zn2P`RH31Va8b@fgA^~_Iv3scX3I~UV^5O^AJf#oVf)tLt%)O_sxN9{?uetJQq(ZZD zR8mokMbeOc&A!`?_;^NDk6lW`vCh~ksKtU|m~oN66yg}Ey*wkm%=fYP*^^Ax==RS3`WfN@W*}VVz z@V_Q80O5L&W|wsyWxRRw#$85xK}9Q>XH~BA=zPt(taJaK*7N`Qv;OnjdMMuTBPOqa 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zMZ>-|MAFG{+3oNsXEqaSqU(B*^$&0S8`B83wanhv5+)XQFC}BHc^lc=fsOCL&U9d{ zJFwu6Db;_P;omp~7}qtPtrR=k>#gZ=80$c%Eq4ueHu-?Vk9N(Q@fdI%=3Ga^R_1^F z^S+zmR`2(Y0D`_fmL>4|5|#92AHHXY>mGr){Dp0IpD~EkAMo_Y$b_hvB1kN3zlrrg zB)++I##y{sspD3p25-@yF~>hwNy5h4$MO>AOUYKRvEp$H`7bbVDhRJV3!yXi*a+YI S3Oxn Date: Wed, 19 Jul 2023 16:20:09 -0400 Subject: [PATCH 08/10] Moved DA-related functions to DA_methods.py. Added additional descriptions. --- notebooks/DA_demo_L96.ipynb | 289 ++++-------------------------------- notebooks/DA_methods.py | 119 ++++++++++++++- 2 files changed, 144 insertions(+), 264 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 611ed9df..cfaf1a9b 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -8,42 +8,6 @@ "# Data Assimilation demo in the Lorenz 96 (L96) two time-scale model\n" ] }, - { - "cell_type": "markdown", - "id": "4c383a2a", - "metadata": {}, - "source": [ - "# Recap of L96 and notation" - ] - }, - { - "cell_type": "markdown", - "id": "2b0a10bb", - "metadata": { - "user_expressions": [] - }, - "source": [ - "{cite}`Lorenz1995` describes a two-time scale dynamical system using two equations which are:\n", - "\n", - "\\begin{align}\n", - "\\frac{d}{dt} X_k\n", - "&= - X_{k-1} \\left( X_{k-2} - X_{k+1} \\right) - X_k + F - \\left( \\frac{hc}{b} \\right) \\sum_{j=0}^{J-1} Y_{j,k}\n", - "\\\\\n", - "\\frac{d}{dt} Y_{j,k}\n", - "&= - cbY_{j+1,k} \\left( Y_{j+2,k} - X_{j-1,k} \\right) - c Y_{j,k} + \\frac{hc}{b} X_k\n", - "\\end{align}\n", - "\n", - "where $X_k$, $k=0,\\ldots,K-1$, denotes the _large scale_ with $K$ degrees of freedom. The $k$ index is periodic, meaning $k=K$ is referring to $k=0$, $k=-1$ is referring to $k=K-1$, and so on. The $j$ indices represent a sub-division of each $k$-element denoting that the $J$ $Y$-values are coupled to a single $X$ value. When $(j+1,k)$ refers to a value beyond $J$, it cycles and refers back to the first value $(1,k+1)$. The slow time-scale queation is forced by the parameter $F$, which determines the chaotic behaviour of the system {cite}`Wilks2005`. The overall structure is illustrated in Fig. 1.\n", - "\n", - "\n", - "```{figure} https://www.researchgate.net/publication/319201436/figure/fig1/AS:869115023589376@1584224577926/Visualisation-of-a-two-scale-Lorenz-96-system-with-J-8-and-K-6-Global-scale-values.png\n", - ":width: 400px\n", - ":name: l96-equation-figure-da-demo\n", - "\n", - "*Visualisation of a two-scale Lorenz '96 system with J = 8 and K = 6. Global-scale variables ($X_k$) are updated based on neighbouring variables and on the local-scale variables ($Y_{j,k}$) associated with the corresponding global-scale variable. Local-scale variabless are updated based on neighbouring variables and the associated global-scale variable. The neighbourhood topology of both local and global-scale variables is circular. Image from [Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures - Scientific Figure on ResearchGate.](https://www.researchgate.net/figure/Visualisation-of-a-two-scale-Lorenz-96-system-with-J-8-and-K-6-Global-scale-values_fig1_319201436)*.\n", - "```" - ] - }, { "cell_type": "markdown", "id": "c33e3435", @@ -51,7 +15,7 @@ "source": [ "# What is DA? Why do we do it?\n", "\n", - "Data assimilation is an approach for combining data (observations) with prior knowledge (from a physical model) to obtain an estimate of the true state of a system. We use data assimilation to generate accurate initial conditions for weather and climate predictions, and to produce reanalysis products (state estimates) of the atmosphere-ocean-sea ice-land system. \n", + "Data assimilation is an approach for combining data (e.g. observations) with prior knowledge (e.g. from a physical model) to obtain an estimate of the true state of a system. We use data assimilation to generate accurate initial conditions for weather and climate predictions, and to produce reanalysis products (state estimates) of the atmosphere-ocean-sea ice-land system. \n", "\n", "Conceptually, data assimilation follows the Bayes' Rule:\n", "\n", @@ -59,7 +23,7 @@ "\\ P(X|Obs)=\\frac{P(Obs|X)P(X)}{P(Obs)}\n", "\\end{align}\n", "\n", - "where $P(X|Obs)$ is the posterior distribution, or the analysis in DA terms, and $P(X)$ is the prior distribution, or the forecast in DA terms. $P(Obs|X)$ is the observation distribution given the prior. Below is a simple schematic representation of one DA step.\n", + "where $X$ is the state of the dynamic system, $P(X|Obs)$ is the posterior distribution, or the analysis in DA terms, and $P(X)$ is the prior distribution, or the forecast in DA terms. $P(Obs|X)$ is the observation distribution given the prior. Simply speaking, we want to know the best estimate of the current state $X$ of the system given the available observations. Below is a simple schematic representation of one DA step.\n", "\n", "```{figure} figs/DA_step.png\n", "```\n" @@ -72,7 +36,7 @@ "source": [ "# Design of the data assimilation experiments in L96\n", "\n", - "We use the 2-scale L96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". This is what we call an idealized biased-model framework in DA research. Our DA model is biased compared to our truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", + "We use the 2-scale Lorenz-96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". Detailed description of this setup can be find here (https://m2lines.github.io/L96_demo/notebooks/gcm-analogue.html). This is what we call an idealized biased-model framework in DA research, in the sense that our DA model is biased compared to the truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", "\n", "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", "1. Generate a “truth” signal from 2-scale L96 model\n", @@ -95,7 +59,7 @@ "id": "66584b6f", "metadata": {}, "source": [ - "# 1. Define variables and functions to use throughout notebook" + "# 1. Define our \"GCM\" and DA parameters to use throughout notebook" ] }, { @@ -113,6 +77,7 @@ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from L96_model import L96, RK4, L96_2t_xdot_ydot, L96_eq1_xdot, L96s\n", + "import DA_methods\n", "\n", "rng = np.random.default_rng()" ] @@ -140,7 +105,7 @@ " dt = 0.005 # Model timestep\n", " si = 0.005 # Truth sampling interval\n", " seasonal = False # Option for adding a seasonal cycle to the forcing in the L96 truth model\n", - " B_loc = 5 # Spatial localization radius for DA\n", + " B_loc = 5 # Spatial localization radius for DA in terms of model grid points\n", " DA = \"EnKF\" # DA method\n", " nens = 500 # Number of ensemble members for DA\n", " inflate_opt = \"relaxation\" # Method for DA model covariance inflation\n", @@ -158,34 +123,6 @@ " # fmt: on" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "3824759d-3678-4915-9793-55595d0989e8", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def observation_operator(K, l_obs, t_obs, i_t):\n", - " \"\"\"Observation operator to map between model and observation space,\n", - " assuming linearity and model space observations.\n", - "\n", - " Args:\n", - " K: spatial dimension of the model\n", - " l_obs: spatial positions of observations on model grid\n", - " t_obs: time positions of observations\n", - " i_t: the timestep of the current DA cycle\n", - "\n", - " Returns:\n", - " Operator matrix (K * observation_density, K)\n", - " \"\"\"\n", - " n = l_obs.shape[-1]\n", - " H = np.zeros((n, K))\n", - " H[range(n), l_obs[t_obs == i_t]] = 1\n", - " return H" - ] - }, { "cell_type": "code", "execution_count": null, @@ -224,156 +161,6 @@ " return hist, time" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "4e65b0ea-ba54-406e-878c-39b46e776022", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def get_dist(i, j, K):\n", - " \"\"\"Compute the absolute distance between two element indices\n", - " within a square matrix of size (K x K)\n", - "\n", - " Args:\n", - " i: the ith row index\n", - " j: the jth column index\n", - " K: shape of square array\n", - "\n", - " Returns:\n", - " Distance\n", - " \"\"\"\n", - " return abs(i - j) if abs(i - j) <= K / 2 else K - abs(i - j)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5ab2c12b-3b13-4557-9228-60222de7470c", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def gaspari_cohn(distance, radius):\n", - " \"\"\"Compute the appropriate distance dependent weighting of a\n", - " covariance matrix, after Gaspari & Cohn, 1999 (https://doi.org/10.1002/qj.49712555417)\n", - "\n", - " Args:\n", - " distance: the distance between array elements\n", - " radius: localization radius for DA\n", - "\n", - " Returns:\n", - " distance dependent weight of the (i,j) index of a covariance matrix\n", - " \"\"\"\n", - " if distance == 0:\n", - " weight = 1.0\n", - " else:\n", - " if radius == 0:\n", - " weight = 0.0\n", - " else:\n", - " ratio = distance / radius\n", - " weight = 0.0\n", - " if ratio <= 1:\n", - " weight = (\n", - " -(ratio**5) / 4\n", - " + ratio**4 / 2\n", - " + 5 * ratio**3 / 8\n", - " - 5 * ratio**2 / 3\n", - " + 1\n", - " )\n", - " elif ratio <= 2:\n", - " weight = (\n", - " ratio**5 / 12\n", - " - ratio**4 / 2\n", - " + 5 * ratio**3 / 8\n", - " + 5 * ratio**2 / 3\n", - " - 5 * ratio\n", - " + 4\n", - " - 2 / 3 / ratio\n", - " )\n", - " return weight" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "86f93dee-eea4-44e0-9ad6-113ab0912688", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def localize_covariance(B, loc=0):\n", - " \"\"\"Localize the model climatology covariance matrix, based on\n", - " the Gaspari-Cohn function.\n", - "\n", - " Args:\n", - " B: Covariance matrix over a long model run 'M_truth' (K, K)\n", - " loc: spatial localization radius for DA\n", - "\n", - " Returns:\n", - " Covariance matrix scaled to zero outside distance 'loc' from diagonal and\n", - " the matrix of weights which are used to scale covariance matrix\n", - " \"\"\"\n", - " M, N = B.shape\n", - " X, Y = np.ix_(np.arange(M), np.arange(N))\n", - " dist = np.vectorize(get_dist)(X, Y, M)\n", - " W = np.vectorize(gaspari_cohn)(dist, loc)\n", - " return B * W, W" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "fc3b629d-398b-4b96-9d63-e95eaab8f688", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def running_average(X, N):\n", - " \"\"\"Compute running mean over a user-specified window.\n", - "\n", - " Args:\n", - " X: Input vector of arbitrary length 'n'\n", - " N: Size of window over which to compute mean\n", - "\n", - " Returns:\n", - " X averaged over window N\n", - " \"\"\"\n", - " if N % 2 == 0:\n", - " N1, N2 = -N / 2, N / 2\n", - " else:\n", - " N1, N2 = -(N - 1) / 2, (N + 1) / 2\n", - " X_sum = np.zeros(X.shape)\n", - " for i in np.arange(N1, N2):\n", - " X_sum = X_sum + np.roll(X, int(i), axis=0)\n", - " return X_sum / N" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "e6a648d4-d5af-419c-bdaa-9dd81b14cffe", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def find_obs(loc, obs, t_obs, l_obs, period):\n", - " \"\"\"NOTE: This function is for plotting purposes only.\"\"\"\n", - " t_period = np.where((t_obs[:, 0] >= period[0]) & (t_obs[:, 0] < period[1]))\n", - " obs_period = np.zeros(t_period[0].shape)\n", - " obs_period[:] = np.nan\n", - " for i in np.arange(len(obs_period)):\n", - " if np.any(l_obs[t_period[0][i]] == loc):\n", - " obs_period[i] = obs[t_period[0][i]][l_obs[t_period[0][i]] == loc]\n", - " return obs_period" - ] - }, { "cell_type": "markdown", "id": "6d3052af", @@ -495,7 +282,7 @@ "user_expressions": [] }, "source": [ - "Now, we generate climatological background (temporal) covariance for the 2-scale L96 model" + "Now, we generate climatological background (temporal) covariance `B_clim2` for the 2-scale L96 model." ] }, { @@ -572,7 +359,7 @@ "user_expressions": [] }, "source": [ - "Generating climatological background covariance for 1-scale L96 model" + "Generating climatological background covariance `B_clim1` for 1-scale L96 model. This climatological covariance will be used by the 3-dimensional variational (3DVar) DA method, or by the hybrid 3DVar-EnKF method. Since we cannot observe every state variable at every possible location, when assimilting sparse observations into the model, we need to use each observation to update multiple model locations, usually around the observed location. The covariance are thus needed to project the model-observation misfits between different model locations in certain DA methods such as 3DVar and EnKF." ] }, { @@ -599,7 +386,7 @@ "source": [ "# 3. Generate synthetic observations\n", "\n", - "Here we generate a set of sparse observations by sampling from the `X_truth` run and adding some random Gaussian noise." + "Here we generate a set of sparse observations by sampling from the `X_truth` run and adding some random Gaussian noise. The observations are stored as individual samples, each containing the time, location, and value." ] }, { @@ -633,7 +420,7 @@ "user_expressions": [] }, "source": [ - "The covariance matrix over the observations `R` (used to express the uncertainty in the observations during DA) is given as a diagonal matrix with entries defined by the square of the \"observational error standard deviation\"." + "The covariance matrix `R` for the observations (used to express the uncertainty in the observations during DA) is given as a diagonal matrix with entries defined by the square of the \"observational error standard deviation\". $R$ is a diagonal matrix because we assume that the errors of different observations are independent. The function `find_obs` is used here to find the locations and values of a set of observations given the observed times. " ] }, { @@ -662,7 +449,7 @@ "plt.plot(range(1000, 1500), X_truth[1000:1500, 0], label=\"truth\")\n", "plt.scatter(\n", " t_obs[100:150, 0],\n", - " find_obs(0, X_obs, t_obs, l_obs, [t_obs[100, 0], t_obs[150, 0]]),\n", + " DA_methods.find_obs(0, X_obs, t_obs, l_obs, [t_obs[100, 0], t_obs[150, 0]]),\n", " color=\"k\",\n", " label=\"obs\",\n", ")\n", @@ -676,36 +463,9 @@ "user_expressions": [] }, "source": [ - "# 4. Apply Localization to the Background Model Covariance\n", - "\n", - "The covariance of the model climatology was computed a-priori from a long run. In this step we apply the localized weighting to the covariance matrix." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5f5501b8-82d7-428a-a030-47d8c50fc4bb", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import importlib\n", - "\n", - "import DA_methods\n", + "# 4. Check the Model Background Covariances for the variable `X`\n", "\n", - "importlib.reload(DA_methods);" - ] - }, - { - "cell_type": "markdown", - "id": "eb095211-2a3f-47c1-899c-ecd4bc4a802d", - "metadata": { - "tags": [], - "user_expressions": [] - }, - "source": [ - "Load pre-calculated climatological background covariance matrix from a long simulation" + "The climatological covariances of both the \"truth\" (2-scale L96) and \"GCM\" (1-scale L96) are computed a-priori from a long run. " ] }, { @@ -717,8 +477,6 @@ }, "outputs": [], "source": [ - "B_loc, W_clim = localize_covariance(B_clim1, loc=Config.B_loc)\n", - "\n", "B_corr1 = np.zeros(B_clim1.shape)\n", "B_corr2 = np.zeros(B_clim2.shape)\n", "for i in range(B_clim1.shape[0]):\n", @@ -810,6 +568,11 @@ }, "outputs": [], "source": [ + "# Localize the covariance matrix in advance to avoid the calculation at each DA step\n", + "# The localization weight matrix is also saved for EnKF\n", + "\n", + "B_loc, W_clim = DA_methods.localize_covariance(B_clim1, loc=Config.B_loc)\n", + "\n", "if Config.param_DA:\n", " mean_param = np.zeros((int(Config.ns_da / Config.DA_freq), len(Config.GCM_param)))\n", " spread_param = np.zeros((int(Config.ns_da / Config.DA_freq), len(Config.GCM_param)))\n", @@ -868,7 +631,7 @@ " # Call DA\n", " t_DA[cycle] = t_truth[i_t]\n", " if Config.DA == \"EnKF\":\n", - " H = observation_operator(Config.K, l_obs, t_obs, i_t)\n", + " H = DA_methods.observation_operator(Config.K, l_obs, t_obs, i_t)\n", "\n", " # Augment state vector with parameters when doing parameter estimation\n", " if Config.param_DA:\n", @@ -897,7 +660,7 @@ " ens_param = X_post[-len(Config.GCM_param) :, :]\n", "\n", " elif Config.DA == \"HyEnKF\":\n", - " H = observation_operator(Config.K, l_obs, t_obs, i_t)\n", + " H = DA_methods.observation_operator(Config.K, l_obs, t_obs, i_t)\n", " B_ens = (\n", " np.cov(X_prior) * (1 - Config.hybrid_factor)\n", " + B_clim1 * Config.hybrid_factor\n", @@ -910,7 +673,7 @@ "\n", " elif Config.DA == \"3DVar\":\n", " X_prior = np.squeeze(X_prior)\n", - " H = observation_operator(Config.K, l_obs, t_obs, i_t)\n", + " H = DA_methods.observation_operator(Config.K, l_obs, t_obs, i_t)\n", " X_post = DA_methods.Lin3dvar(X_prior, X_obs[t_obs == i_t], H, R, B_loc, 3)\n", "\n", " elif Config.DA == \"Replace\":\n", @@ -1014,7 +777,7 @@ "X_inc_ave = X_inc / Config.DA_freq / Config.si\n", "axes[0, 2].plot(M_truth.k, X_inc_ave.mean(axis=(0, -1)), label=\"Inc\")\n", "axes[0, 2].plot(\n", - " M_truth.k, running_average(X_inc_ave.mean(axis=(0, -1)), 7), label=\"Inc Ave\"\n", + " M_truth.k, DA_methods.running_average(X_inc_ave.mean(axis=(0, -1)), 7), label=\"Inc Ave\"\n", ")\n", "axes[0, 2].plot(\n", " M_truth.k,\n", @@ -1046,7 +809,7 @@ ")\n", "axes[1, 0].scatter(\n", " t_DA[plot_start_DA - 1 : plot_end_DA - 1],\n", - " find_obs(plot_x, X_obs, t_obs, l_obs, [plot_start, plot_end]),\n", + " DA_methods.find_obs(plot_x, X_obs, t_obs, l_obs, [plot_start, plot_end]),\n", " label=\"obs\",\n", ")\n", "axes[1, 0].grid(which=\"both\", linestyle=\"--\")\n", @@ -1058,7 +821,7 @@ " for i, c in zip(np.arange(len(Config.GCM_param), 0, -1), [\"r\", \"b\", \"g\", \"k\"]):\n", " axes[1, 1].plot(\n", " t_DA,\n", - " running_average(mean_param[:, i - 1], 100),\n", + " DA_methods.running_average(mean_param[:, i - 1], 100),\n", " c + \"-\",\n", " label=\"C{} {:3f}\".format(\n", " i - 1, mean_param[int(len(t_DA) / 2) :, i - 1].mean()\n", @@ -1066,13 +829,13 @@ " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " running_average(mean_param[:, i - 1] + spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(mean_param[:, i - 1] + spread_param[:, i - 1], 100),\n", " c + \":\",\n", " label=f\"SD {spread_param[int(len(t_DA) / 2):, i - 1].mean():3f}\",\n", " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " running_average(mean_param[:, i - 1] - spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(mean_param[:, i - 1] - spread_param[:, i - 1], 100),\n", " c + \":\",\n", " )\n", " axes[1, 1].legend()\n", diff --git a/notebooks/DA_methods.py b/notebooks/DA_methods.py index e35faba5..edc6c714 100644 --- a/notebooks/DA_methods.py +++ b/notebooks/DA_methods.py @@ -1,10 +1,127 @@ """ Data assimilation methods -Adapted form PyDA project: https://github.com/Shady-Ahmed/PyDA +Partly adapted form PyDA project: https://github.com/Shady-Ahmed/PyDA Reference: https://www.mdpi.com/2311-5521/5/4/225 """ import numpy as np from numba import njit +def observation_operator(K, l_obs, t_obs, i_t): + """Observation operator to map between model and observation space, + assuming linearity and model space observations. + + Args: + K: spatial dimension of the model + l_obs: spatial positions of observations on model grid + t_obs: time positions of observations + i_t: the timestep of the current DA cycle + + Returns: + Operator matrix (K * observation_density, K) + """ + n = l_obs.shape[-1] + H = np.zeros((n, K)) + H[range(n), l_obs[t_obs == i_t]] = 1 + return H + +def get_dist(i, j, K): + """Compute the absolute distance between two element indices + within a square matrix of size (K x K) + + Args: + i: the ith row index + j: the jth column index + K: shape of square array + + Returns: + Distance + """ + return abs(i - j) if abs(i - j) <= K / 2 else K - abs(i - j) + +def gaspari_cohn(distance, radius): + """Compute the appropriate distance dependent weighting of a + covariance matrix, after Gaspari & Cohn, 1999 (https://doi.org/10.1002/qj.49712555417) + + Args: + distance: the distance between array elements + radius: localization radius for DA + + Returns: + distance dependent weight of the (i,j) index of a covariance matrix + """ + if distance == 0: + weight = 1.0 + else: + if radius == 0: + weight = 0.0 + else: + ratio = distance / radius + weight = 0.0 + if ratio <= 1: + weight = ( + -(ratio**5) / 4 + + ratio**4 / 2 + + 5 * ratio**3 / 8 + - 5 * ratio**2 / 3 + + 1 + ) + elif ratio <= 2: + weight = ( + ratio**5 / 12 + - ratio**4 / 2 + + 5 * ratio**3 / 8 + + 5 * ratio**2 / 3 + - 5 * ratio + + 4 + - 2 / 3 / ratio + ) + return weight + +def localize_covariance(B, loc=0): + """Localize the model climatology covariance matrix, based on + the Gaspari-Cohn function. + + Args: + B: Covariance matrix over a long model run 'M_truth' (K, K) + loc: spatial localization radius for DA + + Returns: + Covariance matrix scaled to zero outside distance 'loc' from diagonal and + the matrix of weights which are used to scale covariance matrix + """ + M, N = B.shape + X, Y = np.ix_(np.arange(M), np.arange(N)) + dist = np.vectorize(get_dist)(X, Y, M) + W = np.vectorize(gaspari_cohn)(dist, loc) + return B * W, W + +def running_average(X, N): + """Compute running mean over a user-specified window. + + Args: + X: Input vector of arbitrary length 'n' + N: Size of window over which to compute mean + + Returns: + X averaged over window N + """ + if N % 2 == 0: + N1, N2 = -N / 2, N / 2 + else: + N1, N2 = -(N - 1) / 2, (N + 1) / 2 + X_sum = np.zeros(X.shape) + for i in np.arange(N1, N2): + X_sum = X_sum + np.roll(X, int(i), axis=0) + return X_sum / N + +def find_obs(loc, obs, t_obs, l_obs, period): + """NOTE: This function is for plotting purposes only.""" + t_period = np.where((t_obs[:, 0] >= period[0]) & (t_obs[:, 0] < period[1])) + obs_period = np.zeros(t_period[0].shape) + obs_period[:] = np.nan + for i in np.arange(len(obs_period)): + if np.any(l_obs[t_period[0][i]] == loc): + obs_period[i] = obs[t_period[0][i]][l_obs[t_period[0][i]] == loc] + return obs_period @njit def Lin3dvar(ub, w, H, R, B, opt): From e0fe8029696f8b14d2282ff167077ab05ca70799 Mon Sep 17 00:00:00 2001 From: Feiyu Lu Date: Wed, 19 Jul 2023 16:33:13 -0400 Subject: [PATCH 09/10] Reorganized the DA steps --- notebooks/DA_demo_L96.ipynb | 100 ++++++++++++++++-------------------- 1 file changed, 44 insertions(+), 56 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index cfaf1a9b..8dd81f90 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -39,16 +39,14 @@ "We use the 2-scale Lorenz-96 model as our truth, or our representation of the \"real world\". We then use the 1-scale L96 model as our DA model, or our representation of the \"GCM\". Detailed description of this setup can be find here (https://m2lines.github.io/L96_demo/notebooks/gcm-analogue.html). This is what we call an idealized biased-model framework in DA research, in the sense that our DA model is biased compared to the truth, similar to real-world situations where our GCMs are biased against the natural weather or climate systems. \n", "\n", "We will follow the follwing steps when doing DA in this idealized biased L96 framework:\n", - "1. Generate a “truth” signal from 2-scale L96 model\n", - "2. Specify a biased “GCM”model for performing DA\n", - " * Choose P (to start, use GCM with P=0).\n", - " * Choose F_GCM (to start, use F_GCM=F).\n", + "1. Specify a biased “GCM” model for performing DA, and set the parameters for the \"GCM\", observations, and DA method in `Config`.\n", + " * Parameters to experiment in `Config`: forcing `F`, seasonal cycle, experiment length, \n", + "2. Generate a “truth” signal from the 2-scale L96 model\n", "3. Collect sparse and noisy observations, sampled from “truth”\n", - " * Specify observation density in space, frequency in time\n", - " * Specify observational error\n", + " * Parameters to experiment in `Config`: observation density in space, frequency in time, observational error\n", "4. Perform DA using a method of choice\n", - " * Choose DA method: EnKF, 3DVAR, Hybrid EnKF\n", - " * Specify DA setup: ensemble members, localization, inflation\n", + " * Parameters to experiment in `Config`: DA method (EnKF, 3DVAR, Hybrid EnKF), DA frequency, ensemble size (for EnKF), localization, inflation method and factor\n", + " * Optional: parameter estimation to recover the true forcing\n", "5. Assess DA performance\n", " * RMSE of DA experiment relative to truth\n", "6. Analyze DA increments to assess GCM model error (optional)\n" @@ -85,11 +83,47 @@ { "cell_type": "code", "execution_count": null, - "id": "e2c3e7af", + "id": "ebf223e6-ed8a-425a-b808-55b0cc59c69c", "metadata": { "tags": [] }, "outputs": [], + "source": [ + "def GCM(X_init, F, dt, nt, param=[0]):\n", + " \"\"\"A toy `General Circulation Model` (GCM) that uses the single time-scale Lorenz 1996 model\n", + " with a parameterised coupling term to represent the interaction between the observed coarse\n", + " scale processes `X` and unobserved fine scale processes `Y` of the two time-scale model.\n", + "\n", + " Args:\n", + " X_init: Initial conditions of X\n", + " F: Forcing term\n", + " dt: Sampling frequency of the model\n", + " nt: Number of timesteps for which to run the model\n", + " param: Weights to give to the coupling term\n", + "\n", + " Returns:\n", + " Model output for all variables of X at each timestep along with the corresponding time units\n", + " \"\"\"\n", + " time, hist, X = (\n", + " dt * np.arange(nt + 1),\n", + " np.zeros((nt + 1, len(X_init))) * np.nan,\n", + " X_init.copy(),\n", + " )\n", + " hist[0] = X\n", + "\n", + " for n in range(nt):\n", + " X = X + dt * (L96_eq1_xdot(X, F) - np.polyval(param, X))\n", + " hist[n + 1], time[n + 1] = X, dt * (n + 1)\n", + "\n", + " return hist, time" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3d2efdbe", + "metadata": {}, + "outputs": [], "source": [ "class Config:\n", " # fmt: off\n", @@ -123,44 +157,6 @@ " # fmt: on" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "ebf223e6-ed8a-425a-b808-55b0cc59c69c", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def GCM(X_init, F, dt, nt, param=[0]):\n", - " \"\"\"A toy `General Circulation Model` (GCM) that uses the single time-scale Lorenz 1996 model\n", - " with a parameterised coupling term to represent the interaction between the observed coarse\n", - " scale processes `X` and unobserved fine scale processes `Y` of the two time-scale model.\n", - "\n", - " Args:\n", - " X_init: Initial conditions of X\n", - " F: Forcing term\n", - " dt: Sampling frequency of the model\n", - " nt: Number of timesteps for which to run the model\n", - " param: Weights to give to the coupling term\n", - "\n", - " Returns:\n", - " Model output for all variables of X at each timestep along with the corresponding time units\n", - " \"\"\"\n", - " time, hist, X = (\n", - " dt * np.arange(nt + 1),\n", - " np.zeros((nt + 1, len(X_init))) * np.nan,\n", - " X_init.copy(),\n", - " )\n", - " hist[0] = X\n", - "\n", - " for n in range(nt):\n", - " X = X + dt * (L96_eq1_xdot(X, F) - np.polyval(param, X))\n", - " hist[n + 1], time[n + 1] = X, dt * (n + 1)\n", - "\n", - " return hist, time" - ] - }, { "cell_type": "markdown", "id": "6d3052af", @@ -463,7 +459,7 @@ "user_expressions": [] }, "source": [ - "# 4. Check the Model Background Covariances for the variable `X`\n", + "# Check the Model Background Covariances for the variable `X`\n", "\n", "The climatological covariances of both the \"truth\" (2-scale L96) and \"GCM\" (1-scale L96) are computed a-priori from a long run. " ] @@ -923,14 +919,6 @@ " X_inc_ave=X_inc_ave,\n", " )" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1e96ab6d-95db-4882-ab8c-687b0f9c68bd", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From 0951d3ef9266c17945a243ab2ebc85c9ed763b9c Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Wed, 2 Aug 2023 18:05:40 +0000 Subject: [PATCH 10/10] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- notebooks/DA_demo_L96.ipynb | 12 +++++++++--- notebooks/DA_methods.py | 7 +++++++ 2 files changed, 16 insertions(+), 3 deletions(-) diff --git a/notebooks/DA_demo_L96.ipynb b/notebooks/DA_demo_L96.ipynb index 8dd81f90..d35ba368 100644 --- a/notebooks/DA_demo_L96.ipynb +++ b/notebooks/DA_demo_L96.ipynb @@ -773,7 +773,9 @@ "X_inc_ave = X_inc / Config.DA_freq / Config.si\n", "axes[0, 2].plot(M_truth.k, X_inc_ave.mean(axis=(0, -1)), label=\"Inc\")\n", "axes[0, 2].plot(\n", - " M_truth.k, DA_methods.running_average(X_inc_ave.mean(axis=(0, -1)), 7), label=\"Inc Ave\"\n", + " M_truth.k,\n", + " DA_methods.running_average(X_inc_ave.mean(axis=(0, -1)), 7),\n", + " label=\"Inc Ave\",\n", ")\n", "axes[0, 2].plot(\n", " M_truth.k,\n", @@ -825,13 +827,17 @@ " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " DA_methods.running_average(mean_param[:, i - 1] + spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(\n", + " mean_param[:, i - 1] + spread_param[:, i - 1], 100\n", + " ),\n", " c + \":\",\n", " label=f\"SD {spread_param[int(len(t_DA) / 2):, i - 1].mean():3f}\",\n", " )\n", " axes[1, 1].plot(\n", " t_DA,\n", - " DA_methods.running_average(mean_param[:, i - 1] - spread_param[:, i - 1], 100),\n", + " DA_methods.running_average(\n", + " mean_param[:, i - 1] - spread_param[:, i - 1], 100\n", + " ),\n", " c + \":\",\n", " )\n", " axes[1, 1].legend()\n", diff --git a/notebooks/DA_methods.py b/notebooks/DA_methods.py index edc6c714..6f49fe10 100644 --- a/notebooks/DA_methods.py +++ b/notebooks/DA_methods.py @@ -5,6 +5,7 @@ import numpy as np from numba import njit + def observation_operator(K, l_obs, t_obs, i_t): """Observation operator to map between model and observation space, assuming linearity and model space observations. @@ -23,6 +24,7 @@ def observation_operator(K, l_obs, t_obs, i_t): H[range(n), l_obs[t_obs == i_t]] = 1 return H + def get_dist(i, j, K): """Compute the absolute distance between two element indices within a square matrix of size (K x K) @@ -37,6 +39,7 @@ def get_dist(i, j, K): """ return abs(i - j) if abs(i - j) <= K / 2 else K - abs(i - j) + def gaspari_cohn(distance, radius): """Compute the appropriate distance dependent weighting of a covariance matrix, after Gaspari & Cohn, 1999 (https://doi.org/10.1002/qj.49712555417) @@ -76,6 +79,7 @@ def gaspari_cohn(distance, radius): ) return weight + def localize_covariance(B, loc=0): """Localize the model climatology covariance matrix, based on the Gaspari-Cohn function. @@ -94,6 +98,7 @@ def localize_covariance(B, loc=0): W = np.vectorize(gaspari_cohn)(dist, loc) return B * W, W + def running_average(X, N): """Compute running mean over a user-specified window. @@ -113,6 +118,7 @@ def running_average(X, N): X_sum = X_sum + np.roll(X, int(i), axis=0) return X_sum / N + def find_obs(loc, obs, t_obs, l_obs, period): """NOTE: This function is for plotting purposes only.""" t_period = np.where((t_obs[:, 0] >= period[0]) & (t_obs[:, 0] < period[1])) @@ -123,6 +129,7 @@ def find_obs(loc, obs, t_obs, l_obs, period): obs_period[i] = obs[t_period[0][i]][l_obs[t_period[0][i]] == loc] return obs_period + @njit def Lin3dvar(ub, w, H, R, B, opt): # The solution of the 3DVAR problem in the linear case requires

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