U.S. Department of the Interior U.S. Geological Survey Lake Evaporation using Energy Budget Method: Walker Lake, NV - a case study In cooperation with Bureau of Reclamation Kip K. Allander 2008 USGS National Ground-Water Workshop August 4, 2008 Lakewood, CO

Outline Why lake evaporation is important. Overview of different methods. Energy budget method. Case study – Evaporation from Walker lake, NV. Some useful references.

Why is evaporation from Lakes important? Water budgets. Water budgets. Evaporation is often large discharge component of lake water budget. Evaporation is often large discharge component of lake water budget. Water management. Water management. Leads to better understanding of other water budget components such as ground water. Leads to better understanding of other water budget components such as ground water. Lake water quality. Lake water quality.

Methods Water budget Water budget Potential ET Potential ET Pan Evaporation Pan Evaporation Energy budget Energy budget

Energy Budget Method Q n : Net radiation Q v : Heat advection Q b : Net energy stored in lake-bed sediments -Assumed negligible in deeper lakes Q e : Energy used for evaporation Q h : Sensible heat Q w : Energy advected by evaporation Q x : Change in heat storage in lake

Energy Budget Method - continued ρ : Density of water (10 3 kg m -3 ) E : Evaporation rate (m/s) L : Latent heat of vaporization (J kg -1 ) B : Bowen ratio (unitless) c : Heat capacity for water (J kg -1 °C -1 ) T e : Temperature of evaporated water, taken as lake surface temperature ( T 0 ; °C) T b : Base temperature reference, usually 0 (°C)

Net Radiation ( Q n ) Critical component that is central driver of evaporation process. Critical component that is central driver of evaporation process. One of the easier components to measure. One of the easier components to measure. Measure directly using a net radiometer. Measure directly using a net radiometer.

Heat Advection ( Q v ) F x : Flux of water by process. Inflows and outflows of SW, GW, Precipitation (m s -1 ) T x : Temperature of water flux (°C)

Heat Advection ( Q v ) - Inflow What is needed to measure Q v inflow? What is needed to measure Q v inflow? Measure inflow and T of SW. Measure inflow and T of SW. Measure or estimate GW inflow and T. Measure or estimate GW inflow and T. T of precipitation is wet bulb T during precip events. T of precipitation is wet bulb T during precip events.

Heat Advection ( Q v ) - Outflow What is needed to measure Q v outflow? What is needed to measure Q v outflow? Measure outflow of SW, T can be estimated from Lake T. Measure outflow of SW, T can be estimated from Lake T. Measure estimate GW outflow T can be estimated from lake T. Measure estimate GW outflow T can be estimated from lake T. Heat advected by evaporation is already incorporated into governing equation. Heat advected by evaporation is already incorporated into governing equation.

Heat Storage ( Q x ) Layer 1 Layer 2 Layer 3 Layer n c : Heat capacity for water (4,187 J kg -1 °C -1 ) ρ : Density of water (10 3 kg m -3 ) t : Time of measurement period (s) d i : Thickness of layer (m) A i : Area of layer (m 2 ); A 0 : Lake surface area (m 2 ) ΔT i : Change in temperature of layer (°C)

Heat Storage ( Q x ) What is needed to measure Q x ? What is needed to measure Q x ? Lake bathymetry. Lake bathymetry. Temperature profile measurements every 1 to 4 weeks. Temperature profile measurements every 1 to 4 weeks.

Bowen Ratio ( B ) P : Atmospheric Pressure (Pa) C a : Specific heat of air (J kg -1 °C -1 ) T 0 : Water surface temperature ( °C ) T u : Temperature of air at height above lake surface ( °C ) e 0 : Vapor pressure at lake water/air interface (Pa) e u : Vapor pressure at height above lake surface (Pa)

Lake surface temperature ( T 0 ) Critical component of calculation. Critical component of calculation. Is also one of the easier components to measure. Is also one of the easier components to measure. Measure directly using thermistor. Measure directly using thermistor.

Evaporation from Walker Lake Background Background Problem Problem Objectives Objectives Data Data Results Results Summary Summary

Walker River Basin - Background Walker River Basin is a topographically closed basin with DA of 3,950 mi 2. Walker River Basin is a topographically closed basin with DA of 3,950 mi 2. Source of Walker River is in the Eastern Sierra Mountains, a humid continental climate with high annual precipitation. Source of Walker River is in the Eastern Sierra Mountains, a humid continental climate with high annual precipitation.

Walker River Basin - Background Supports large agricultural economy in four valleys on its journey downstream. Supports large agricultural economy in four valleys on its journey downstream. Terminates in Walker Lake, a terminal lake (no surface outflow) set in mid-latitude desert climate, with low annual precipitation and hot, dry summers. Terminates in Walker Lake, a terminal lake (no surface outflow) set in mid-latitude desert climate, with low annual precipitation and hot, dry summers.

Walker Lake E – Problem Lake is in decline due to diversions of source water to upstream AG. Lake is in decline due to diversions of source water to upstream AG. Salt mass is relatively constant leading to increasing TDS. Salt mass is relatively constant leading to increasing TDS. Freshwater fishery is severely stressed, entire lake ecology is threatened. Freshwater fishery is severely stressed, entire lake ecology is threatened. Water is needed to preserve ecology of lake, but how much? Water is needed to preserve ecology of lake, but how much?

Walker Lake E – Problem Original estimate of E was developed using water budget method. Original estimate of E was developed using water budget method. Potential problems with original estimate: Potential problems with original estimate: Assumed GW was negligible. Assumed GW was negligible. Stream inflow based on record a substantial distance from Walker Lake. Stream inflow based on record a substantial distance from Walker Lake. Uncertainty on how streamflow was converted to depth measurement. Uncertainty on how streamflow was converted to depth measurement.

Walker Lake Stage Hydrograph for unused well 4.5 miles south of Walker Lake Walker Lake E – Problem 42 ft decline in ground- water level (~0.3 ft/yr)

Walker Lake E - Objectives Determine evaporation from Walker Lake. Determine evaporation from Walker Lake. Develop an improved water budget for Walker Lake. Develop an improved water budget for Walker Lake.

Walker Lake E - Data Platform installed Nov 2004 and operated through Nov Platform installed Nov 2004 and operated through Nov Water temperature profiles measured approximately every month for entire period. Water temperature profiles measured approximately every month for entire period.

Walker Lake E – Data Heat storage

Walker Lake E – Data Energy budget summary

Walker Lake E – Results E by energy budget periods

Walker Lake E – Results E by month

Walker Lake E – Results Discharge by E

Walker Lake E – Summary Walker Lake is a terminal lake in recession which is threatening ecologic collapse. Walker Lake is a terminal lake in recession which is threatening ecologic collapse. An accurate water budget is necessary for decisions on how to save Walker Lake while minimizing impact on AG economy. An accurate water budget is necessary for decisions on how to save Walker Lake while minimizing impact on AG economy. Evaporation from Walker Lake is greater than previously thought by about 25,000 ac-ft/yr. Evaporation from Walker Lake is greater than previously thought by about 25,000 ac-ft/yr. Groundwater as a source of inflow to Walker Lake is greater than previously thought. Groundwater as a source of inflow to Walker Lake is greater than previously thought.

Open water evaporation – References Click on box to open a short, incomplete list of references related to lake evaporation energy-budget method.