Pustam | पुस्तम | পুস্তম🇳🇵<p>Basics of Numerical Weather Prediction (NWP):</p><p>1. THE HORIZONTAL MOMENTUM EQUATION:<br>\[<br>\frac{d\mathbf{V}}{dt} + f\hat{k} \times \mathbf{V} = -\nabla \phi + \frac{\sigma}{p_s} \frac{\partial \phi}{\partial \sigma} \nabla p_s + \mathbf{F}<br>\]</p><p>2. THE CONTINUITY EQUATION:<br>\[<br>\frac{\partial p_s}{\partial t} + \nabla \cdot (p_s \mathbf{V}) + \frac{\partial}{\partial \sigma}(p_s \dot{\sigma}) = 0<br>\]</p><p>3. THE THERMODYNAMIC ENERGY EQUATION:<br>\[<br>\frac{1}{R} \frac{d}{dt} \left[ \sigma \frac{\partial \phi}{\partial \sigma} \right] + \frac{RT}{C_p p} \left[ p_s \dot{\sigma} + \sigma\dot{p_s} \right] = -Q<br>\]</p><p>4. HYDROSTATIC EQUATION:<br>\[<br>\frac{\partial \phi}{\partial \sigma} = -\frac{RT_v}{\sigma}<br>\]</p><p>5. SURFACE PRESSURE TENDENCY EQUATION:<br>\[\displaystyle<br>\frac{\partial p_s}{\partial t} = -\int_{0}^{1} \nabla\cdot (p_s \mathbf{V}) \, d\sigma<br>\]</p><p>6. MOISTURE EQUATION:<br>\[\displaystyle<br>\frac{\partial}{\partial t} (p_s q) + \nabla\cdot (p_s q \mathbf{V}) + \frac{\partial}{\partial \sigma} (p_s q \dot{\sigma}) = p_s S<br>\]</p><p>The six primary unknowns are: \(\mathbf{V}\) (horizontal wind velocity), \(p_s\) (surface pressure), \(T\) (temperature), \(q\) (specific humidity or moisture), \(\phi\) (geopotential), and \(\dot{\sigma}\) (sigma velocity or vertical velocity in \(\sigma\)-coordinates).</p><p><a href="https://mathstodon.xyz/tags/NWP" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NWP</span></a> <a href="https://mathstodon.xyz/tags/Weather" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Weather</span></a> <a href="https://mathstodon.xyz/tags/NumericalWeatherPrediction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumericalWeatherPrediction</span></a> <a href="https://mathstodon.xyz/tags/Meteorology" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Meteorology</span></a> <a href="https://mathstodon.xyz/tags/Climate" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Climate</span></a> <a href="https://mathstodon.xyz/tags/ClimateScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ClimateScience</span></a> <a href="https://mathstodon.xyz/tags/Earth" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Earth</span></a> <a href="https://mathstodon.xyz/tags/EarthScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EarthScience</span></a> <a href="https://mathstodon.xyz/tags/ClimateChange" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ClimateChange</span></a> <a href="https://mathstodon.xyz/tags/ClimateSciences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ClimateSciences</span></a> <a href="https://mathstodon.xyz/tags/Science" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Science</span></a> <a href="https://mathstodon.xyz/tags/WeatherPrediction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WeatherPrediction</span></a> <a href="https://mathstodon.xyz/tags/Humidity" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Humidity</span></a> <a href="https://mathstodon.xyz/tags/Moisture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Moisture</span></a> <a href="https://mathstodon.xyz/tags/Pressure" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Pressure</span></a> <a href="https://mathstodon.xyz/tags/Velocity" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Velocity</span></a> <a href="https://mathstodon.xyz/tags/SurfacePressure" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SurfacePressure</span></a> <a href="https://mathstodon.xyz/tags/HydrostaticEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HydrostaticEquation</span></a> <a href="https://mathstodon.xyz/tags/WeatherPrediction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WeatherPrediction</span></a> <a href="https://mathstodon.xyz/tags/Ocean" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Ocean</span></a> <a href="https://mathstodon.xyz/tags/Atmosphere" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Atmosphere</span></a> <a href="https://mathstodon.xyz/tags/AOS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AOS</span></a> <a href="https://mathstodon.xyz/tags/ClimateDynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ClimateDynamics</span></a> <a href="https://mathstodon.xyz/tags/WeatherDynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WeatherDynamics</span></a> <a href="https://mathstodon.xyz/tags/Geopotential" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Geopotential</span></a> <a href="https://mathstodon.xyz/tags/SigmaVelocity" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SigmaVelocity</span></a> <a href="https://mathstodon.xyz/tags/VerticalVelocity" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>VerticalVelocity</span></a> <a href="https://mathstodon.xyz/tags/MoistureEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MoistureEquation</span></a> <a href="https://mathstodon.xyz/tags/Thermodynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Thermodynamics</span></a> <a href="https://mathstodon.xyz/tags/Dynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Dynamics</span></a> <a href="https://mathstodon.xyz/tags/NavierStokes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NavierStokes</span></a></p>