Week 3 Atmospheric Water PDF

Atmospheric Water CHAPTER 2 INTRODUCTION TO PHYSICAL HYDROLOGY BY MARTIN HENDRIKS PART II, SECTION 4 PHYSICAL HYDROLOGY S. LAWRENCE DINGMAN MINA FAGHIH 2025.01.20 Overview of Atmospheric Water Importance of atmospheric water in the hydrologic...

Atmospheric Water CHAPTER 2 INTRODUCTION TO PHYSICAL HYDROLOGY BY MARTIN HENDRIKS PART II, SECTION 4 PHYSICAL HYDROLOGY S. LAWRENCE DINGMAN MINA FAGHIH 2025.01.20 Overview of Atmospheric Water Importance of atmospheric water in the hydrological cycle Key processes: precipitation, evaporation, condensation Role in maintaining Earth's water balance  Introduction to Cloud Formation Clouds are visible masses of tiny liquid water droplets or ice crystals suspended in the atmosphere, formed from condensed water vapor. Clouds form when moist air rises and cools, leading to condensation. The cooling occurs due to adiabatic expansion, where the air pressure decreases as altitude increases. Key ingredients for cloud formation: water vapor, cooling mechanism, and condensation nuclei.  Mechanisms Driving Air Upward Four main lifting mechanisms: Convection Orographic lifting Frontal lifting. Convergence Convection Definition: Convective precipitation occurs when the sun heats the Earth's surface, causing the air above it to rise. ,Whether convection leads to precipitation depends on the stability of the atmosphere. Results from surface heating causing atmospheric instability. Rising warm air cools, condenses, and forms precipitation. Process: Surface heating → Warm air uplift → Cooling at dry adiabatic lapse rate (Γda). If moisture is sufficient, cooling continues at the saturated adiabatic rate (Γsat), forming clouds and rain. Key Features: Small-scale, intense rainfall. Often accompanied by lightning, thunder, and hail. Orographic Precipitation Definition: Orographic Precipitation occurs when air is forced to rise over a topographic barrier such as a mountain range.. Process: Uplift on windward slopes → Cooling → Cloud formation → Rainfall. Lee side: Adiabatic warming causes a rain shadow. Examples: Cherrapunji, India: Highest annual rainfall globally (11,872 mm). Mt. Waialeale, Hawaii: 11,684 mm annual rainfall. Factors: Elevation, slope steepness, wind speed, and humidity. Orographic Precipitation Frontal Lifting and Cloud Formation Definition: Frontal lifting occurs when two air masses of different temperatures and densities meet, causing the warmer, less dense air to rise over the cooler, denser air. Types of Fronts and Cloud Formation: Warm Front: Cold Front: Warm air gradually rises over a cold air mass. Cold air forces warm air to rise rapidly. Produces stratiform clouds (e.g., cirrus, altostratus, produces cumuliform clouds (e.g., cumulus nimbostratus). cumulonimbus). Associated with widespread, steady precipitation. Associated with intense, short-lived precipitation and thunderstorms. Frontal Lifting Convergence Precipitation and Cloud Formation Definition: Convergence precipitation occurs when air flows from different directions meet, forcing the air to rise. This upward motion cools the air, leading to cloud formation and precipitation. Converging Airflows: In low-pressure areas, the atmospheric pressure at the surface is lower than in the surrounding regions. This pressure difference drives air to move horizontally from high-pressure areas toward the low- pressure zone in an attempt to equalize the pressure. This movement of air toward the low-pressure center is called surface convergence.. Cooling and Condensation: Rising air expands and cools.Water vapor condenses into water droplets, forming clouds. Key Features of Convergence Clouds: Produces cumuliform clouds (e.g., cumulus, cumulonimbus). Associated with heavy rain, thunderstorms, and sometimes severe weather. Common in the tropics (e.g., Intertropical Convergence Zone, ITCZ). Occult Precipitation Definition: refers to a type of precipitation that does not fall from clouds but is instead derived from atmospheric water vapor condensing directly onto surfaces. It is common in environments where moisture from the air interacts with vegetation or other objects, contributing to the local water balance. Types: Rime Ice: In colder regions, supercooled water droplets freeze upon contact with surfaces, forming frost-like ice. Fog Drip: In cloud forests, droplets from fog condense on leaves and drip to the ground, acting as an essential water source for the ecosystem. Dew: Moisture from the air condenses on surfaces during cool nights, especially when surfaces cool below the dew point.  Common Weather Mechanism Description Cloud Types Patterns Warm air rises due to Localized thunderstorms, Convection Cumuliform (e.g., cumulus) surface heating. intense rain Air is forced to rise over a Rain on windward side, dry Orographic Lifting topographic barrier like a Stratiform and cumuliform on leeward side mountain. Warm air is forced over cold Widespread precipitation, Frontal Lifting Stratiform or cumuliform air at a front. thunderstorms Airflows from different Cumuliform (e.g., Heavy rain, thunderstorms, Convergence directions meet and rise. cumulonimbus) ITCZ phenomena Precipitation formed by Adds to moisture in water vapor condensing Occult Precipitation No distinct cloud formation ecosystems (e.g., forests in directly onto surfaces (e.g., humid areas) fog drip). Cold Clouds and Warm Clouds in Hydrology Feature Cold Clouds Warm Clouds Above 0°C (liquid water Temperature Below 0°C (ice crystals) droplets) Higher altitudes (upper Lower altitudes (lower to Altitude troposphere) middle troposphere) Rain, drizzle, or light Precipitation Type Snow, hail, or freezing rain precipitation Main Precipitation Ice crystal process (Bergeron Collision-coalescence process Process process) Stratus, Cumulus, Cloud Examples Cirrus, Cumulonimbus Nimbostratus Introduction to Precipitation Formation Precipitation forms through the condensation of water vapor into liquid water or ice that becomes heavy enough to fall under gravity. Two main processes: collision-coalescence and Bergeron process. Requires three conditions: Moist air. Cooling mechanism. Presence of condensation nuclei.  The Collision-Coalescence Process Occurs in warm clouds (temperature above freezing). Larger water droplets fall faster, colliding with smaller droplets, causing them to grow. Dominates in tropical and low-latitude regions.  The Bergeron Process Occurs in cold clouds (temperature below freezing). Relies on differences in saturation vapor pressure over ice and liquid water. Ice crystals grow at the expense of surrounding water droplets. Dominates in mid- and high-latitude regions. Types of Clouds and Their Formation Cloud types based on altitude and appearance: Cumulus: Fluffy, white clouds formed by Cirrus: High, thin, wispy clouds formed by ice convection crystals. Nimbus: Rain-producing clouds, often combined with other types (e.g., cumulonimbus).. Stratus: Layered, gray clouds formed by stable air.  Measurement of Precipitation Significance: Precipitation is the input for the land phase of the hydrologic cycle. Accurate measurement is critical for hydrologic analyses (e.g., flood forecasting, model calibration). Measurement accuracy concerns must be addressed for reliable analysis. Observation Methods: Point Measurements: Traditional rain gauges Area Measurements: Radar and satellite. Combined techniques improve area-based estimations. Precipitation Gauges Point Measurement Types: A. Nonrecording Gauges : A type of precipitation or water-level measuring instrument that provides data at a single point in time but does not continuously record the measurements. These gauges are essentially containers that collect precipitation. The depth is measured periodically, often enhanced with a funnel for better precision Key Characteristics: 1.No Continuous Data: These gauges do not keep an ongoing record of precipitation or water levels over time. 2.Manual Observation: Users must check the gauge and write down the measurements, such as the amount of rainfall or water level, at specific intervals. 3.Simple Design: Nonrecording gauges are typically simpler and less expensive compared to recording gauges. B. Recording Gauges: a) Weighing Gauges: Track accumulated weight. b) Float-siphon Gauges: Use floats to measure water levels. c) Tipping-Bucket Gauges: Count tip events. Comparison Table Float-Siphon Tipping-Bucket Feature Weighing Gauges Gauges Gauges Measures weight Float and siphon Tipping buckets for Mechanism directly system fixed volumes Moderate (low in Accuracy High Moderate heavy rainfall) Maintenance High Moderate Low All precipitation Moderate-heavy Light to moderate Sensitivity types rainfall rainfall Varying rainfall Standard monitoring Applications Research stations regions stations Struggles with light Underestimates Limitation Prone to vibrations rain intense rainfall C. Advanced Technologies: Optical Gauges: Measure light disturbances. Capacitance Gauges: Record water-induced capacitance changes. Disdrometers: Measure drop size and momentum. Accuracy Considerations: Errors from wind, evaporation, and splashing cause biases. Guidelines by WMO help minimize errors through proper siting and calibration. Challenges in Point Measurements Systematic Errors: Systematic errors are biases that consistently affect measurements. Wind deflection can lead to significant underestimation, especially for snow. Similarly, evaporation and splashing introduce additional inaccuracies Random Errors: Random errors often arise from inconsistencies in calibration, siting, or human reporting. Proper maintenance and following siting guidelines can significantly minimize these errors.“. Solutions:Use of reference gauges (e.g., ground-level gauges and DFIR). Radar Measurement Applications Modern radar technologies, like dual-polarization, provide detailed information, distinguishing rain from snow. These are critical in weather prediction and flood warnings. Satellite Measurement Satellites play a critical role in monitoring precipitation on a global scale. They provide comprehensive coverage, especially in remote areas where ground-based instruments like rain gauges and radar are unavailable. Advantages of Satellite Precipitation Measurement Global Reach: Covers areas inaccessible to ground-based instruments. Temporal Continuity: Provides consistent data over time for trend analysis. Multi-Scale Data: Offers insights on local, regional, and global precipitation patterns. Comparison of Precipitation Measurement Methods Method Advantages Limitations High precision at specific Point Limited spatial coverage sites Real-time, large area Signal attenuation, Radar coverage calibration needed Indirect measurement, lower Satellite Global coverage resolution Areal Estimation from Point Measurements Definition: Areal estimation calculates precipitation over a region based on point measurements. Importance: Critical for hydrologic modeling, water resource planning, and flood prediction. Methods Overview: ✓ Direct Weighted Averages. ✓ Spatial Interpolation (Surface Fitting). ✓ Comparison of Methods. Direct Weighted Averages Concept: Assign weights to point measurements based on their relevance to the area. Key Methods: ✓Arithmetic Mean ✓Thiessen Polygons ✓Isohyetal Method Direct Weighted Averages: Arithmetic Mean Formula: 𝑃avg : Average precipitation. 𝑃𝑖 : Precipitation at gauge 𝑖. 𝑛: Number of gauges. Assumptions:Uniform precipitation distribution across the area.  Direct Weighted Averages: Thiessen Polygons It assigns weights to precipitation measurements based on the area of influence surrounding each rain gauge. Advantages: Accounts for spatial distribution of gauges. Straightforward to apply in regions with well- distributed gauges. Limitations: Assumes precipitation is uniform within each polygon, which may not reflect reality. Less effective in areas with uneven gauge spacing or highly variable precipitation. Steps to Create Thiessen Polygons 1. Locate Gauges: Plot the locations of all precipitation gauges on a map. 2.Draw Perpendicular Bisectors: For every pair of adjacent gauges, draw a line connecting them and construct a perpendicular bisector. 3.Define Polygons: The bisectors divide the map into polygons, with each gauge at the center of its polygon. 4.Assign Precipitation: Assume the precipitation value within each polygon is the same as that measured at the gauge located in the polygon. Direct Weighted Averages: Thiessen Polygons Formula: 𝑃area : Areal precipitation. 𝑃𝑖: Precipitation at gauge 𝑖. 𝑤𝑖 : Weight based on polygon area 𝐴𝑖. Ai: Area of the polygon associated with gauge i. 𝐴 total : Total area. Divide the area into polygons around each gauge, using the nearest neighbor rule.  Direct Weighted Averages: Isohyetal Method The areas between isohyets are used to calculate a weighted average. Advantages and Limitations Advantages: Captures spatial variability in precipitation. Provides more accurate estimates compared to simpler methods like arithmetic mean or Thiessen polygons. Limitations: Requires detailed spatial data and precise drawing of isohyets. Time-consuming and labor-intensive, especially for large or complex areas. Direct Weighted Averages: Isohyetal Method Steps: 1.Draw isohyets (contours of equal precipitation). 2.Calculate area between consecutive isohyets. 3.Weight precipitation by these areas. Formula: Pi: Average precipitation between isohyets. Ai: Area between isohyets. Areal Estimation from Point Measurements Definition: Areal estimation calculates precipitation over a region based on point measurements. Importance: Critical for hydrologic modeling, water resource planning, and flood prediction. Methods Overview: ✓ Direct Weighted Averages. ✓ Spatial Interpolation (Surface Fitting). ✓ Comparison of Methods. Spatial Interpolation (Surface Fitting) Spatial interpolation is a method used to estimate precipitation at unsampled locations by creating a continuous surface based on point measurements from rain gauges. Purpose: Estimate precipitation at unmeasured locations. Key Methods: Inverse Distance Weighting (IDW). Spline Interpolation. Kriging. Spatial Interpolation:Inverse Distance Weighting (IDW) Inverse Distance Weighting (IDW) is a spatial interpolation method used to estimate values at unsampled locations based on values from nearby sampled points. The method assumes that points closer to the prediction location have a greater influence than those farther away P(x): Precipitation at location x. Pi: Precipitation at gauge i. di: Distance from x to gauge i. p: Power parameter (typically p=2). Spatial Interpolation: Spline Interpolation What is a Spline? A spline is a piecewise-defined polynomial function that is used to model data smoothly. The most commonly used type of spline in spatial interpolation is the cubic spline, which fits a cubic polynomial to intervals between data points. spline interpolation fits a smooth, continuous function (usually polynomial) to the data points. This method is particularly useful when the data exhibits smooth and continuous spatial variation, as it ensures a smooth surface that passes through all given data points. Spatial Interpolation: Kriging Concept: Geostatistical method incorporating spatial correlation. Key Features: Based on a statistical models that account for spatial autocorrelation. Provides uncertainty estimates. Formula: Kriging weights depend on spatial covariance between points. Comparison of Areal Estimation Methods Summary Direct Weighted Averages: Simple but limited in spatial resolution. Key Points: IDW: Direct methods (e.g., Isohyetal) are intuitive and practical. Easy to implement but sensitive to distance Spatial interpolation (e.g., Kriging) offers weighting. better precision. Spline: Method selection depends on terrain, data Smooth but oversmooths extremes. density, and computational resources. Combining methods often yields the best Kriging: results. Statistically robust but resource-intensive.