Week 8 - Spatial Interpolation

Spatial Interpolation using three different methods.
Los Angeles County Rainfall calculation

Introduction

This exercise uses rainfall data from 58 Los Angeles County station for the purpose of creating some interpolated maps of the region about trends in precipitations and its distribution by interpolation of existing data.
The datasets available for rainfall for both current and average normal seasons in Los Angeles County Area are limited to 58 points, which have been manually entered and geographically located through X-Y coordinates definition and taken from the Los Angeles Water Resources Department under "Near real-time precipitation map" (complete list given below at bottom page).
The following list of datasets includes three different methodologies of interpolation analysis, each with different characteristics and quality results, able to give a clear idea of trends and current situation of rainfall for this area. These methods are the IDW method, the Natural Neighbor method and the Kriging method.

Rainfall: Current Season

The above map shows the rainfall as in 25th February 2011 for the current season.
No matters the method used for calculations, it is possible to see how the Eastern
area of the County, corresponding to the Los Angeles Padres Forest, has bigger amounts
of rainfall. This could be related with the fact that many of the stations in that area are located
at higher elevations, where altitude may have influenced amounts of rainfall and then
the amount of vegetation grown in that National Forest. On the other hand, desertic and internal areas have as expected the lesser amounts of rain. There is an augment in coastal areas where micro climates influence rainfall.
The Inverse distance method has as a result a map showing several "islands" of different values
within neighbor limits of those stations having higher values than the rest of the areas more conformal and balanced to the general trends. This can cause several cases of exceptions and gives more weight to the singular records, and so resulting in a map showing several exceptions and a general trend less conform.
The Natural Neighbor method is represented in map two. Here, the trends and the values look shared more equally within all the map, causing less prominence of singular differences compared with the previous map. I think it that in this case, given the fact that the distribution of rainfall within the territory has a simple spatial organization, this is the best of the three methods described for overall three analysis. The fact that one point is closer to a particular station has a strong relationship also in how close is the amount of rainfall to that same station.
Other factors calculated in weighed methods are less precise than this.
Kriging method shows in this case a precision that could be compared with the Natural Neighbor method, and creates Contour lines that are equally shared within the middle-points areas and finally very realistic.

Rainfall: Historic mean of Los Angeles County

The second map shows the rainfall of a normal season in Los Angeles County. It is inmediately clear that the third case, the Kriging analysis show a map of precipitation substantially different form the other two. This is because in the normal values have been created with a mean calculation process that didn't allow the record of higher peaks of rain in one single station (which have been recorded in more than one case between the current season records).
Kriging analysis had furthermore smoothed and flattened these values, creating a map overall more flattened and with no peaks of value.
By comparing the second maps with the first ones, it is possible to see how rainfall during this current season has been lower than the average historic rainfall. It is possible to recognize also in this case regions where vegetation is more likely to grow and desert areas at North where rainfall is extremely low.
Also in this case, Natural Neighbor Interpolation method produced more equally shared distribution and contour lines of levels of rainfall rather than the Inverse Distance Weighted.

Rainfall: Mapping the Difference within current and historical rainfall

The last map above shows the difference between the current amount of rainfall and the average records for the Los Angeles County area. Blue colors indicate higher rainfall than normal, while Red/Orange values are areas receiving less rain than usual.
Natural Neighbor and IDW methods are methods showing a similar pattern, both indicating as there has been an increase in Western and Southern areas of the County, which correspond to the Los Angeles Padres Forest and the Coastal shoreline between Venice and Long Beach.
Not much has changed instead for the desert areas North of the County. Most of the County however had received much less amounts of rain than expected and probably is affecting reservoirs closer to most urbanized areas. These are in fact located at South-West, where most of the red areas created by the interpolation are located.
In this case, the flattening resulted with the Kraging interpolation method had shared the rainfall more equally within the southern areas and has given probably the most defined map of the differences between the two datasets as a result of the Interpolation.

Table of Records

NAME	ID Number	LAT		LONG	Elevation feet	Current S.	Normal S.	Difference S.	Elevation mts.
Acton Camp Precip	58	34.450556		-118.198333	2,625.00	6.65	10.03	-3.38	800.10
Agoura Precip	56	34.135556		-118.751944	800	13.7	17.84	-4.14	243.84
Aliso Canyon Precip	57	34.328333		-118.554722	2,367.00	20.16	22.82	-2.66	721.46
Aliso Canyon Wagon Wheel	4	34.274722		-118.526389	1112	17.13	19.57	-2.44	338.94
Avek Precip	54	34.539167		-117.923056	2,825.00	6.06	5.78	0.28	861.06
Ballona Crk Precip	55	33.998611		-118.401389	38	8.94	12.39	-3.45	11.58
Bell Canyon (Rocketdyne) Precip	52	34.178056		-118.590833	2,260.00	14.02	14.74	-0.72	688.85
Bell Cyn Debris Basin Precip	53	34.194167		-118.656389	895	12.28	15.57	-3.29	272.80
Big Pines Recreation Park Pcp	50	34.378889		-117.688889	6,860.00	26.73	24.5	2.23	2,090.93
Big Rock Mesa Precip	51	34.039167		-118.616667	300	19.65	16.58	3.07	91.44
Big Tujunga-camp15 Precip	46	34.289167		-118.288056	1,525.00	13.74	19.36	-5.62	464.82
Bouquet Cyn @ Urban Precip	47	34.448333		-118.505833	1,300.00	9.88	7.98	1.9	396.24
Brand Park Precip	48	34.188056		-118.271944	1,250.00	14.17	18.34	-4.17	381.00
Brown's Canyon Precip	49	34.311667		-118.607222	2,400.00	19.25	19.55	-0.3	731.52
Cedar Springs Precip	42	34.355833		-117.873333	6,780.00	30.16	29.95	0.21	2,066.54
Chilao-St Hwy Precip	43	34.317778		-118.008056	5,275.00	20.75	22.9	-2.15	1,607.82
Clear Crk School Precip	44	34.276944		-118.17	3,150.00	27.52	30.54	-3.02	960.12
Cogswell Dam Precip	45	34.243333		-117.963333	2,300.00	25.47	34.21	-8.74	701.04
Domin Wat Co Precip	39	33.831389		-118.224722	30	13.9	12.11	1.79	9.14
DP WHQ	1	34.081667		-118.150278	466	18.5	16.82	1.68	142.04
Eagle Rock Rsvr Precip	40	34.145556		-118.19	1,085.00	16.34	18.14	-1.8	330.71
Eaton Wash Precip	41	34.074722		-118.054722	261	16.26	12.4	3.86	79.55
Flintridge Precip	38	34.181667		-118.185556	1,600.00	23.03	22.09	0.94	487.68
LA 96th & Cen. Precip	36	33.948889		-118.254444	121	12.99	13.78	-0.79	36.88
LA Ducommun St Precip	37	34.0525		-118.236667	306	13.54	15.63	-2.09	93.27
La Mirada Precip	28	33.883056		-118.016667	75	9.33	13.45	-4.12	22.86
La Rvr @ Wardlow Precip	29	33.819722		-118.122	25	11.3	9.9	1.4	7.62
La Tuna DB Precip	30	34.236667		-118.326667	1,160.00	12.52	16.44	-3.92	353.57
Lancaster Roper Precip	31	34.679722		-118.010278	2,400.00	7.24	5.34	1.9	731.52
Lancaster Waterworks	3	34.801111		-118.559722	2910	7.24	5.34	1.9	886.97
Le Habra Heights	11	33.960833		-117.950556	755	15.98	15.85	0.13	230.12
Lechuza Pat Sta Precip	32	34.076944		-118.879444	1,620.00	21.85	22.4	-0.55	493.78
Lewis Ranch Precip	33	34.42		-117.886389	4,615.00	17.17	15.21	1.96	1,406.65
Little Gleason Precip	34	34.378333		-118.149167	5,600.00	15.67	23.87	-8.2	1,706.88
Little Rock Crk Above Dam Percip	35	34.478056		-118.023333	3,267.00	9.8	9.16	0.64	995.78
Loomis Ranch Precip	27	34.348333		-118.048056	4,325.00	15.39	18.55	-3.16	1,318.26
Mescal Smith Precip	24	34.4675		-117.711111	3,810.00	9.29	7.8	1.49	1,161.29
Mint Cyn @ Fitch Precip	25	34.446667		-118.4275	1,652.00	9.02	9.05	-0.03	503.53
Monte Nido Fire Precip	26	34.077778		-118.692222	600	19.65	22	-2.35	182.88
Newhall-Sol Precip	21	34.425833		-118.578333	1,243.00	13.74	17.89	-4.15	378.87
North Lancaster Precip	22	34.761389		-118.125	2,310.00	2.68	5.19	-2.51	704.09
Northridge- LADPW Precip	23	34.231111		-118.541111	1,117.00	12.8	15.3	-2.5	340.46
Pacoima Dam Precip	20	34.33		-118.399444	1,950.00	17.2	19.54	-2.34	594.36
Palmdale Water Dist Precip	17	34.594722		-118.091944	2,595.00	7.17	6.93	0.24	790.96
Pine Canyon Patrol Station Pcp	18	34.673333		-118.429167	3,286.00	17.24	19.14	-1.9	1,001.57
Pnt Vicen Ligh Precip	19	33.741667		-118.410556	125	18.87	11.07	7.8	38.10
Pudd Div Precip	15	34.129167		-117.780833	1,130.00	20.43	19.21	1.22	344.42
Quartz Hill Precip	16	34.648056		-118.24	2,395.00	9.96	7.97	1.99	730.00
Redman Precip	14	34.764444		-117.925	2,360.00	5.59	5.18	0.41	719.33
Relay	2	34.735		-117.776944	3057	6.52	5.15	1.37	931.77
Rocky Buttes Precip	13	34.65		-117.863333	2,540.00	6.57	4.84	1.73	774.19
San Gab Pow House Precip	12	34.155556		-117.907778	744	16.16	22.98	-6.82	226.77
San Gabriel Dam Precip	7	34.205556		-117.860556	1,481.00	28.78	28.86	-0.08	451.41
San Gabriel East Fork Percip	8	34.235833		-117.805	1,600.00	25.55	26.04	-0.49	487.68
Sanberg Airways Station Precip	9	34.746389		-118.724167	3,635.00	10.94	12.85	-1.91	1,107.95
Santa Anita Dam Precip	10	34.184167		-118.019722	1,400.00	27.17	26.21	0.96	426.72
Tanbark Precip	6	34.205278		-117.760833	2,750.00	43.66	28.04	15.62	838.20
Topanga Canyon Patrol Station Pcp	5	34.084167		-118.599167	745	18.89	24.42	-5.53	227.08