Changes from the original module are written in bold text
Distributes temperatures to HRUs using a lapse rate computed from daily measured data at two temperature stations.
The inverse of the square of the distance between an HRU and each weather station. Does not need to be input because it is calculated. Identified as parameter because not a state variable. Units are the square of the input unit for the hru_xlong, hru_ylat, tsta_xlong, and tsta_ylat parameters (see below).
The elevation difference between each (ntemp) temperature site divided by 1,000. Elevation/1,000 is used for calculating a daily lapse rate for the basin for both maximum and minimum air temperature, in units of feet per feet.
The elevation difference between each HRU and each (ntemp) temperature site divided by a 1,000. Elevation/1,000 is used for the lapse rate calculations between temperature sites and each HRU; accounts for differences in elevation, in units of feet per feet.
The x or longitude of the centroid of a HRU that is input in projection coordinates such as State Plane, Lambert, or UTM. Used to calculate distance between HRU and a weather site. Units can be feet, miles, meters, or kilometers but must be consistent with hru_ylat, tsta_xlong, and tsta_ylat.
The y or latitude of the centroid of a HRU that is input in projection coordinates such as State Plane, Lambert, or UTM. Used to calculate distance between HRU and a weather site. Units can be feet, miles, meters, or kilometers but must be consistent with hru_xlong, tsta_xlong, and tsta_ylat.
Maximum monthly maximum temperature for the basin. Maximum temperatures are not to be above this value. Used as constraint for potentially bad or missing input data values, ° F or ° C, depending on units of data.
Minimum monthly minimum temperature for the basin. Minimum temperatures are not to be below this value. Used as constraint for potentially bad or missing data values, ° F or ° C, depending on units of data.
Mean monthly minimum lapse rate for minimum air temperature used to constrain the lowest lapse rate for a month for minimum temperature. In terms of ° F or ° C, depending on units of data, per 1,000 feet. If a daily calculated lapse rate for minimum temperature is less than this value, it is set equal to this value.
Mean monthly maximum lapse rate for minimum air temperature used to constrain the highest lapse rate for a month for minimum temperature. In terms of ° F or ° C, depending on units of data, per 1,000 feet. If a daily calculated lapse rate for minimum temperature is greater than this value, it is set equal to this value.
Mean monthly minimum lapse rate for maximum air temperature used to constrain the lowest lapse rate for a month for maximum temperature. In terms of ° F or ° C, depending on units of data, per 1,000 feet. If a daily calculated lapse rate for maximum temperature is less than this value, it is set equal to this value.
Mean monthly maximum lapse rate for minimum air temperature used to constrain the highest lapse rate for a month for maximum temperature. In terms of ° F or ° C, depending on units of data, per 1,000 feet. If a daily calculated lapse rate for maximum temperature is greater than this value, it is set equal to this value.
HRU maximum temperature adjustment. Adjustment, in ° F or ° C depending on units of data, to HRU maximum temperature based on slope and aspect of HRU.
HRU minimum temperature adjustment. Adjustment, in ° F or ° C depending on units of data, to HRU minimum temperature based on slope and aspect of HRU.
Elevation of each temperature measurement station, in feet.
The x or longitude of a weather station that is input in projection coordinates such as State Plane, Lambert, or UTM. Used to calculate distance between HRU and a weather site. Units can be feet, miles, meters, or kilometers but must be consistent with hru_ylat, hru_xlong, and tsta_ylat.
The y or latitude of a weather station that is input in projection coordinates such as State Plane (Lambert, UTM). Used to calculate distance between HRU and a weather site. Units can be feet, miles, meters, or kilometers but must be consistent with hru_xlong, tsta_xlong, and hru_ylat.
Total basin area, in acres. [basin]
Area for each HRU, in acres. [basin]
Mean elevation for each HRU, in feet. [basin]
Indicator for units for temperature data, 0= ° F and 1= ° C. [basin]
Basin daily average maximum temperature lapse rate, ° F or ° C depending on units of data, per 1,000 feet.
Basin daily average minimum temperature lapse rate, ° F or ° C depending on units of data, per 1,000 feet.
Basin maximum temperature, ° F or ° C, depending on units of data.
Basin minimum temperature, ° F or ° C, depending on units of data.
Average HRU temperature in ° C.
Average HRU temperature in ° F.
Maximum HRU temperature in ° C.
Maximum HRU temperature in ° F.
Measured maximum temperature at each temperature measurement station, ° F or ° C, depending on units of data. [obs]
Measured minimum temperature at each temperature measurement station, ° F or ° C, depending on units of data. [obs]
Measured daily maximum (tmax) and minimum (tmin) air temperatures are adjusted (interpolated) to account for differences in elevation and slope-aspect between the climate stations and each HRU. Air temperature data and the adjustment parameters must be in the same units as were declared in the basin module. If the computation time step is less than daily, then tmax should equal tmin and represent the average temperature for the time step.
The daily basin average lapse rate for maximum (basin_lapse_max) and minimum (basin_lapse_min) temperature are first computed by:
![basin_lapse_min - [Summation of ((obs_tmin(i) minus obs_tmin(j))) divided by ntemp]](../../images/temp_2sta_prms_dist2-2.gif)
ntemp is the number of temperature stations,
i,j are indexes of temperature stations, with i from 1 through (ntemp-1) and j from i+1 to ntemp,
obs_tmax is the observed maximum temperature for station i and j,
obs_tmin is the observed minimum temperature for station i and j, and
tsta_elev is the elevation of each temperature measurement station.
For the calculation of the daily basin average lapse rates (basin_lapse_max and basin_lapse_min), each of the individual lapse rates between any two stations (e.g., (obs_tmax(1)-obs_max(2))/delv) are checked to determine that they are within the range of the input parameters lapsemin_min, lapsemin_max, lapsemax_min, and lapsemax_max. Rates outside of the range are set to the appropriate minimum or maximum value. For the case in which no temperature data are available, the basin lapse rates are set to the average of the appropriate input parameters described above.
The daily maximum and minimum temperature for an HRU are then interpolated from the weather sites using the basin lapse rates, the elevation difference (elfac) between a temperature site and the HRU, and an inverse distance squared weighting of Dean and Snyder (1977) and Bauer and Vaccaro (1987). The first stemp in interpolating the values is calculating the daily correction factors for maximum (tcrx) and minimum (tcrn) temperature for each HRU, using
i is an index for a temperature station and is from 1 to ntemp, and
hru_elev is the mean elevation for each HRU, in feet.
The daily maximum and minimum temperature (shown below in units of ∞F) for an HRU are then calculated as
![tminf = [Summation of (obs_tmin(i) + tcrx)divided by (Summation of dist)] minus tmin_adj](../../images/temp_2sta_prms_dist2-8.gif)
, i is an index for a temperature station, from 1 to ntemp,
tmax_adj is the HRU maximum temperature adjustment,
tmin_adj is the HRU minimum temperature adjustment, and
dist is the inverse of the square of the distance between a HRU and each weather station. Dist is calculated as
(1. / sqrt((hru_xlong(j)- tsta_xlong(i))**2 + (hru_ylat(i)- tsta_ylat(j) )**2), where each HRU (j) dist is computed for each temperature station (i).
This module also computes a weighted average maximum and minimum temperature for the basin for each time step.
Bauer, H.H., and Vaccaro, J.J., 1987, Documentation of a deep percolation model for estimating ground-water recharge: U. S. Geological Survey Open-File Report 86-536, 180 p.
Dean, J.D., and Snyder, W.M., 1977, Temporally and areally distributed rainfall: Journal of Irrigation Division, American Society of Civil Engineers, TA 103, No. IR2, p. 221-224.
Leavesley, G.H., Lichty, R.W., Troutman, B.M., and Saindon, L.G., 1983, Precipitation-runoff modeling system--User's manual: U. S. Geological Survey Water-Resources Investigations Report 83-4238, 207 p.
URL for this page is http://pubsdata.usgs.gov/pubs/of/2002/ofr02362/htdocs/temp_2sta/temp_2sta_prms_dist2.htm
Page contact: Mark Mastin (mcmastin@usgs.gov),
253-428-3600, ext. 2609
Last modified: Friday, 11-Jan-2013 03:19:58 EST
![basin_lapse_max - [Summation of ((obs_tmax(i) minus obs_tmax(j))) divided by ntemp]](../../images/temp_2sta_prms_dist2-1.gif)
,
and
, 
, ![tmaxf = [Summation of (obs_tmax(i) + tcrx)divided by (Summation of dist)] minus tmax_adj](../../images/temp_2sta_prms_dist2-7.gif)
, and